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This paper synthesizes research on student and teacher emotions in the classroom through the lens of the Ecological Dynamic Systems model. It places emotions in immediate contexts in the classroom including emotionally expressive environment, learning/instruction, and relationships. The paper identifies specific antecedents of emotions within each context. It further discusses how the intersection of classroom events and teachers' and students' goals, beliefs, and relational experiences give rise to emotions. Emotions in the classroom further reflect the complex transactions between classroom and socio-historical contexts. The paper discusses how emotions are influenced by broad socio-cultural factors including educational policies and reforms, school demographics, and culture at large. Finally, it focuses on the role of appraisal for the emotions in the classroom and how appraisals are contextualized by students' and teachers' beliefs and personal experiences. Understanding the interplay of various contexts for emotions in the classroom will inform teacher preparation, designing instructional and behavioral interventions as well as educational policies and reforms. [ABSTRACT FROM AUTHOR]

Runtime verification (RV) refers to methods for formal reasoning about all aspects of the dynamic execution of systems, including hardware, software, and cyber-physical systems. RV includes techniques to assess and enforce correctness of a system against systemic bugs or extrinsic uncertainties. These methods are typically considered lightweight as they may not involve exhaustive verification or proofs, but they provide a higher level of rigor and versatility compared to conventional testing methods. This article introduces the extended versions of selected papers from the peer-reviewed proceedings of the 20th International Conference on Runtime Verification (RV 2020). RV 2020 was supposed to be held in Los Angeles, California, USA in July 2020, but was instead held virtually due to the global Covid-19 pandemic. [ABSTRACT FROM AUTHOR]

Simultaneous Localization and Mapping (SLAM) is one of the research hotspots in the field of robotics, and it is also a prerequisite for autonomous robot navigation. The localization accuracy and stability of traditional SLAM based on static scene assumption declines due to the interference of dynamic objects. To solve the problem, this paper proposes a semantic SLAM system for dynamic environments based on object detection named DO-SLAM. Firstly, DO-SLAM uses YOLOv5 to identify objects in dynamic environments and obtains the semantic information; Then, combined with the outlier detection mechanism proposed in this paper, the dynamic objects are effectively determined and the feature points on the dynamic objects are eliminated; The combination method can reduce the interference of dynamic objects to SLAM, and improve the stability and localization accuracy of the system. At the same time, a static dense point cloud map is constructed for high-level tasks. Finally, the effectiveness of DO-SLAM is verified on the TUM RGB-D dataset. The results show that the Absolute Trajectory Error (ATE) and Relative Pose Error (RPE) are reduced, indicating that DO-SLAM can reduce the interference of dynamic objects. [ABSTRACT FROM AUTHOR]

Let (X , f) be a dynamical system. Using an equivalence relation ∼ on X , we introduce the quotient (X / ∼ , f ⋆) of the dynamical system (X , f) . In the first part of the paper, we give new results about sensitive dependence on initial conditions of (X / ∼ , f ⋆) , transitivity of (X / ∼ , f ⋆) , and periodic points in (X / ∼ , f ⋆) . In the second part of the paper, we use these results to study chaotic functions on the Cantor fan. Explicitly, we study functions f on the Cantor fan C such that (1) (C , f) is chaotic in the sense of Devaney, (2) (C , f) is chaotic in the sense of Robinson but not in the sense of Devaney, and (3) (C , f) is chaotic in the sense of Knudsen but not in the sense of Devaney. We also study chaos on the Lelek fan. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of coordinated control for multiple surface unmanned vehicles in a cluster under the influence of time-varying disturbances such as wind field and tides, based on state feedback controllers. With the rapid development of offshore cluster formation control technology, studying the cluster formation control problem of surface unmanned vehicles in multiple clusters under the influence of wind field and tides in complex and changing sea environments has important practical significance. This paper proposes a complete solution based on the Hamiltonian method. Firstly, each cluster is set to be located within a ellipsoidal virtual container throughout the entire motion process, and the trajectory of the virtual ellipsoid is used as an external state constraint for the cluster. Based on this, the dynamic equation of the system and the corresponding value function under the influence of wind field and tides on the sea surface are established, and the Hamilton–Jacobi–Bellman equation is used to solve the energy constraint and mutual avoidance between clusters and their members to obtain the optimal control and trajectory of each cluster. Finally, numerical simulation results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Flying Ad hoc Networks have emerged as a promising technology for number of real-time applications. However, the flexible and unstructured characteristics of these networks make them vulnerable to security threats posed by malicious nodes, such as denial of service attacks, node impersonation, and information breaches. Another major issue is the consideration of those nodes being unable to prove their trustworthiness due to factors like hardware or software failure, or by link interruptions, during the processing of detection of false nodes in the network. The existing mechanisms encompassing encryption, authentication, and intrusion detection highlight limitations to secure real-time applications and services due to the high speed of flying nodes and the absence of fixed network structures. To overcome these constraints, this research paper incorporates a novel framework for evaluating and improving the security of network by introducing an innovative cluster-based approach. Moreover, it presents a fuzzy model that dynamically estimates the trust levels of both individual nodes and clusters, by assigning weight to the parameters to address vulnerabilities. Additionally, a trust reconfiguration mechanism is further proposed to address the issue of nodes unable to substantiate their trust by providing them with additional chances based on the collective trust from previous evaluations. Further, the paper incorporates a dynamic reputation system to proficiently identify and separate malicious and selfish nodes from the network. Simulation results indicate a significant improvement in performance metrics, with a considerable reduction in delay and drop ratio by 41.46% and 36.37%, respectively, while the sufficient rise of 54.71% and 46.05% in throughput and coverage, respectively, comparing with the considered state-of-art. [ABSTRACT FROM AUTHOR]

This paper is concerned with the well-posedness and asymptotic behavior of solutions for the following extensible beam equation with non-local energy damping u tt + Δ 2 u - κ ϕ (‖ ∇ u ‖ 2 ) Δ u - φ (‖ Δ u ‖ 2 + ‖ u t ‖ 2) Δ u t + f (u) = h. More specifically, this is a complementary work to the paper by Sun and Yang (Discrete Contin Dyn Syst Ser B 27(6):3101–3129, 2022), where the authors consider this model assuming the hypothesis that φ ∈ C 1 (R +) with non-degenerate condition φ (s) > 0 , s ∈ R + . They prove the existence of strong global and exponential attractors and their robustness on the perturbed extensibility parameter κ . In this paper assuming φ (s) ⪆ γ s q which contemplates the degenerate condition φ (0) = 0 , we prove the existence of weak and regular solutions to the problem proposed and employing the method given in Temam (Springer-Verlag, New York, 1998) we show that the dynamic system (X , S t) given by the weak solutions of the problem has a compact global attractor in the weak topology of the phase space X. This class of nonlinear beams arising in connection with models for flight structures with non-local energy damping is proposed by Balakrishnan and Taylor (Proceedings Damping 89, Flight Dynamics Lab and Air Force Wright Aeronautical Labs, WPAFB, 1989). [ABSTRACT FROM AUTHOR]

The purpose of designing embedded Internet of things and studying the ad hoc technology of gateway is to meet the monitoring requirements brought by the continuous expansion of data center. Among them, in the aspect of dynamic data monitoring, this paper designs a dynamic acquisition algorithm, that is, by analyzing the characteristics of data center resources and the number of information acquisition methods, so as to adjust the data acquisition cycle and to reduce the monitoring workload and improve the monitoring flexibility. At the same time, this paper also studies the automatic psychological evaluation system of students. It is found that with the intensification and efficient operation of social competition, some special groups of college students are facing increasing pressure, and events caused by psychological problems emerge one after another. Even though there are many psychological evaluation systems on the network, a large number of psychological knowledge and mental health management on the Internet cannot effectively manage and improve the psychological status of college students. Therefore, the university needs to build a psychological evaluation system for college students in time and combine the automatic psychological evaluation system for college students with embedded Internet of things and cloud service technology to improve the accuracy of psychological evaluation. The application of the system, college students can independently evaluate their own mental state, if there are psychological problems can be timely counseling, not only can improve the level of mental health education in colleges and universities, but also can promote the development of physical and mental health. [ABSTRACT FROM AUTHOR]

The demise of the scholastic worldview and the rise of the mechanistic one may give the impression of a parallel demise of the scholastic explanatory framework. In this paper, I argue that this impression is wrong. To this end, I first outline Descartes' representative and particularly sharp mechanistic criticism of the scholastic notion of explanation. Deploying conceptual machinery from contemporary philosophy of science, I then suggest a reconstruction of the scholastic notion that is immune to Descartes' criticism. Based on this reconstruction, I reinterpret the dispute between Descartes and the scholastics as one that concerns the extent of two legitimate conceptions of explanation. Finally, I outline a contemporary dispute within cognitive neuroscience that reflects the Cartesian-scholastic one as thus reinterpreted, thereby showing that aspects of the world may well require a scholastic-like approach for their explanation. The aim of this paper, then, is to shed light on a most important philosophical-cum-scientific historical controversy from a modern perspective, but also to highlight the deep historical roots of a related contemporary dispute. Based on this, the paper also seeks to draw a substantial philosophical conclusion concerning the issue under dispute in both controversies. [ABSTRACT FROM AUTHOR]

This paper presents a new robust control structure to control a 3-degree-of-freedom (3-DoF) helicopter in the presence of uncertainties, disturbance and actuators saturation. The 3-DoF helicopter is an underactuated system where only two DoFs can be fully controlled, so elevation and pitching motions are considered in this paper. Robust control methods conventionally generate control signals with high amplitude to suppress model uncertainties. Nonetheless, the practical actuators might not be able to supply such control efforts, causing actuator saturation. The actuator saturation phenomenon highly affects the motion control performance of the system and even can cause instability. To address this issue in this paper, firstly a smooth prevention function is utilized as an approximation of the practical actuator saturation, limiting the input torque/force in a prescribed range. However, to avoid violating the stability of the system by a prevention function, it should be considered in the dynamic model of the system, leading to a non-affine structure. Hence, the problem of controlling a non-affine system is addressed by proposing a new third-order dynamic model, as well as a robust control scheme. In this approach, a backstepping control is utilized, equipped with an adaptive radial basis function neural network to estimate and compensate for the adverse terms. Finally, the effectiveness of the proposed scheme is evaluated through a detailed simulation study on a 3-DoF helicopter. [ABSTRACT FROM AUTHOR]

This paper considers the problem of constructing compartmental models of dynamic systems by using a software package for symbolic calculation written in Julia. The software package is aimed at unifying the formalized construction of compartmental models, taking into account the meaningful description of possible interactions among compartments and the influence of various factors on the evolution of systems. An approach to the development of the instrumental and methodological basis for modeling the dynamic systems the behavior of which can be described by one-step processes is developed. The proposed software package enables the symbolic representation of the differential equations of the model in both stochastic and deterministic cases. It is implemented in Julia and uses the Julia Symbolics computer algebra library. A comparison between the Julia Symbolics tools and some other computer algebra systems is carried out. The application of the developed software package to a compartmental model is considered. The results can be used to solve problems of constructing and studying dynamic models in natural sciences that are represented by one-step processes. [ABSTRACT FROM AUTHOR]

Purpose: In gear systems, several parametric studies have shown the great sensitivity of the dynamic behaviour of gear transmission system. However, these parameters admit strong dispersions. Therefore, it becomes necessary to consider these uncertainties to ensure the robustness of the analysis of gear system. In this paper, the angle that the line of the wheels centers makes with the stationary axis is considered as uncertain parameter. Methods: This paper presents uncertainty analysis of two-stage gear system. The Chaos Polynomial method is used to investigate the influence of angle uncertainty on the dynamic response of this system. Meanwhile, the Monte Carlo simulation is employed to verify the suitability and the accuracy of this method. Results: On the basis of the proposed method, the dynamic responses of two-stage gear system with uncertain parameter are presented. Comparative linear displacement amplitudes are illustrated by the Chaos Polynomial method and the Monte Carlo simulation. Conclusions: The Chaos Polynomial method is verified to possess good numerical performance. Results show that uncertain parameter will significantly influence the dynamic response of two-stage gear system. When the standard deviation of uncertain parameter is very small, satisfactory results can be obtained by adopting different order of Polynomial Chaos method. The present study shows that the proposed method allows high uncertainty in the angle parameter, which is the usual requirement in the practical applications. [ABSTRACT FROM AUTHOR]

This paper demonstrates the validity of the Naess–Gadai method for extrapolating extreme value statistics of second-order Volterra series processes through application on a representative model of a deep water small size tension leg platform (TLP), with specific focus on wave sum frequency effects affecting restrained modes: heave, roll and pitch. The wave loading was estimated from a second order diffraction code WAMIT, and the stochastic TLP structural response in a random sea state was calculated exactly using Volterra series representation of the TLP corner vertical displacement, chosen as a response process. Although the wave loading was assumed to be a second order (non-linear) process, the dynamic system was modelled as a linear damped mass-spring system. Next, the mean up-crossing rate based extrapolation method (Naess–Gaidai method) was applied to calculate response levels at low probability levels. Since exact solution was available via Volterra series representation, both predictions were compared in this study, namely the exact Volterra and the approximate one. The latter gave a consistent way to estimate efficiency and accuracy of Naess–Gaidai extrapolation method. Therefore the main goal of this study was to validate Naess–Gaidai extrapolation method by available analytical-based exact solution. Moreover, this paper highlights limitations of mean up-crossing rate based extrapolation methods for the case of narrow band effects, such as clustering, typically included in the springing type of response. [ABSTRACT FROM AUTHOR]

The aim of this paper is to review recently calculus curriculum reforms and research studies that document what types of understanding students develop in their precalculus courses. We argue that it is important to characterize what difficulties students experience to solve tasks that include the use of foundational calculus concepts and to look for possible ways for students to develop a way of reasoning to work on problems that involve variational phenomena. Thus, we identified tasks in which calculus students exhibit limited understanding of essential concepts to approach and solve those tasks. The purpose is to illustrate and discuss how the systematic use of a Dynamic Geometry System (DGS) could provide a set of affordances for students to develop ways of thinking to grasp calculus foundational ideas and to study the derivative concept. Here, we relied on Thurston's seminal work that emphasizes the relevance for learners to identify, connect, and coordinate different dimensions and meanings (intuitive, symbolic, algorithmic, geometric, physical, and formal) to construct, understand, and apply the concept of derivative. [ABSTRACT FROM AUTHOR]

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph. Data-driven approximations of differential equations present a promising alternative to traditional methods for uncovering a model of dynamical systems, especially in complex systems that lack explicit first principles. A recently employed machine learning tool for studying dynamics is neural networks, which can be used for solution finding or discovery of differential equations. However, deploying deep learning models in unfamiliar settings-such as predicting dynamics in unobserved state space regions or on novel graphs-can lead to spurious results. Focusing on complex systems whose dynamics are described with a system of first-order differential equations coupled through a graph, we study generalization of neural network predictions in settings where statistical properties of test data and training data are different. We find that neural networks can accurately predict dynamics beyond the immediate training setting within the domain of the training data. To identify when a model is unable to generalize to novel settings, we propose a statistical significance test. Deep learning is a promising alternative to traditional methods for discovering governing equations, such as variational and perturbation methods, or data-driven approaches like symbolic regression. This paper explores the generalization of neural approximations of dynamics on complex networks to novel, unobserved settings and proposes a statistical testing framework to quantify confidence in the inferred predictions. [ABSTRACT FROM AUTHOR]

This paper focuses on the combined path following (PF) and direct yaw-moment control (DYC) problem of unmanned electric vehicles (UEVs) based on an event-triggered Takagi–Sugeno (T–S) fuzzy method. First, to describe the parameter uncertainties and nonlinear tire dynamics of UEVs, a T–S fuzzy dynamic model is developed for performance analysis and controller design of the vehicle lateral dynamic system. Second, as the signal transmission inevitably suffers from delay and data dropouts because of the limited network bandwidth, an event-triggered scheme is constructed to complete the communication scheduling and save the communication resource. Third, considering that there is an unavoidable asynchronous constraint between the fuzzy system and the fuzzy controller due to the communication delay, a hierarchical event-triggered fuzzy controller design approach is given via a new Lyapunov functional. Moreover, a differential distribution scheme is introduced to obtain the desired torque of each tire of the vehicle. Finally, experimental results validate that the presented controller in this paper is able to improve the path following accuracy by 61.93% with a resource economization 92.04% compared with the existing method. [ABSTRACT FROM AUTHOR]

This article is aimed at developing a target SAP-LAP model for the sustainable development of Russian universities in the Decade of Science and Technologies. To achieve this, we used the methods of trend analysis and correlation analysis of the flexibility and sustainability of Russian universities in 2013–2022. The key question of the paper is how important flexibility is for the achievement of sustainability of Russian universities, and by which tools of change management the required flexibility of Russian universities can be achieved. The contribution to the existing body of knowledge on university management is that the authors proved that flexibility is a source of sustainable development of Russian universities in the Decade of Science and Technologies. This contribution was achieved through the use of the SAP-LAP modeling method, which allows proposing recommendations that adapt to the changing context of Russian universities as dynamic systems. As a result, it is concluded that the Decade of Science and Technologies is a special context for Russian universities' sustainable development. In this context, the sustainability, responsibility and flexibility of Russian universities differ from international patterns. It is advisable to study Russia's system of science and higher education as a dynamic system to most accurately determine and manage the sustainability of Russian universities. The theoretical importance of this paper's results is that they clarified the cause-and-effect links of flexibility and sustainability of Russian universities. The practical importance of the article is that the offered target SAP-LAP model of sustainable development of Russian universities in the Decade of Science and Technologies will maximize their flexibility for the most complete manifestation of their responsibility to the economy for the personnel and technological support of digital modernization and innovative development of Russia. [ABSTRACT FROM AUTHOR]

This paper investigates the variational approach using nabla (denoted as ∇) within the framework of time scales. By employing two different methods, we derive the Euler-Lagrange equations for first-order variational approach to optimization problems involving exponential functions, as well as for those with both exponential functions and their ∇-derivatives. To establish the high-order variational approach to optimization problem, we present the Leibniz Formula for ∇-derivatives along with its proof. Additionally, we determine the high-order variational approach to optimization problem incorporating ∇-derivatives of exponential functions. Through these analyses, we aim to contribute to the understanding and application of the variational calculus on time scales, offering insights into the behavior of dynamic systems governed by exponential functions and their derivatives. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive radial basis function neural network (RBFNN) is investigated and presented for identifying the nonlinear dynamical system. In traditional RBFNN structure, the selections of the activated radius are decided by the designer's experience to satisfy the best approximation of nonlinear dynamical function. In order to reduce the experience error, an adaptive RBFNN mechanism that can realize auto-regulation of activated radius is proposed in this paper. Taking the lattice points as the center of activated function, we use Taylor expansion to separate the factor of activated radius in local space. In order to ensure that the identification error has the property of fast convergence, the error conversion function is used for shrinking the gain in the error differential equation. Constructing a Lyapunov function to determine the differential equation of the weights and the activated radius, it is shown that the weights and the activated radius will converge to the neighborhood of its true value and the identification error will converge to neighborhood of zero in a periodic or period-like nonlinear dynamical system. To illustrate the effectiveness of the proposed adaptive RBFNN, Vanderpol and Duffing dynamical system are used as test examples, in comparison with traditional RBFNN and wavelet neural networks (WNN). The results show that the proposed method has best accurate identification and approximating effect in all of test algorithms. [ABSTRACT FROM AUTHOR]

The theory of compact global attractors for dynamical systems relies on the existence of a bounded absorbing set. In this paper, suppressing this condition, we present sufficient conditions to ensure the existence and uniqueness of maximal attractors for dynamical systems (both autonomous and nonautonomous). Such attractors are, in general, unbounded. For semigroups satisfying these conditions, when a Lyapunov function exists, we also present the characterization of the unique maximal attractor as the unstable set of the critical elements (not necessarily fixed points). As an example we present a semilinear parabolic equation to illustrate the theory in the autonomous case. For the nonautonomous setting, applying the general theory, we present an abstract evolution equation and a concrete parabolic equation as examples. [ABSTRACT FROM AUTHOR]

Various inequivalent notions of attraction for autonomous dynamical systems have been proposed, each of them useful to understand specific aspects of attraction. Milnor's notion of a measure attractor considers invariant sets with positive measure basin of attraction, while Ilyashenko's weaker notion of a statistical attractor considers positive measure points that approach the invariant set in terms of averages. In this paper we propose generalisations of these notions to nonautonomous evolution processes in continuous time. We demonstrate that pullback/forward measure/statistical attractors can be defined in an analogous manner and relate these to the respective autonomous notions when an autonomous system is considered as nonautonomous. There are some subtleties even in this special case–we illustrate an example of a two-dimensional flow with a one-dimensional measure attractor containing a single point statistical attractor. We show that the single point can be a pullback measure attractor for this system. Finally, for the particular case of an asymptotically autonomous system (where there are autonomous future and past limit systems) we relate pullback (respectively, forward) attractors to the past (respectively, future) limit systems. [ABSTRACT FROM AUTHOR]

For a topological dynamical system (X, T), l ∈ N and x ∈ X , let N l (X) and L x l (X) be the orbit closures of the diagonal point (x , ... , x) (l times) under the actions G l and τ l respectively, where G l is generated by T × ... × T (l times) and τ l = T × ... × T l . In this paper, we show that for a minimal system (X, T) and d , l ∈ N , the maximal d-step pro-nilfactor of (N l (X) , G l) is (N l (X d) , G l) , where X d is the d-step pronilfactor of (X, T). Meanwhile, when (X, T) is a minimal nilsystem, we also calculate the pro-nilfactors of the system (L x l (X) , τ l) for almost every x w.r.t. the Haar measure. In particular, there exists a minimal 2-step nilsystem (Y, T) and a countable subset Ω of Y such that for every y ∈ Y \ Ω the maximal equicontinuous factor of (L y 2 (Y) , τ 2) is not (L π 1 (y) 2 (Y 1) , τ 2) , where Y 1 is the maximal equicontinuous factor of (Y, T) and π 1 : Y → Y 1 is the factor map. [ABSTRACT FROM AUTHOR]

This paper studies the classification of large-scale time series data constructed by nonlinear dynamical systems via deterministic learning. Firstly, a large-scale time series dataset including five classes of dynamical patterns is constructed based on the benchmark Lorenz system. Secondly, the performance of the dynamical pattern recognition method based on deterministic learning is evaluated for the time series classification task in the large-scale time series dataset. Last but not least, based on the concept of representative selection and the recent research on the deterministic learning theory, a novel dynamical pattern recognition-based time series classification framework is modified, including: (1) the selection of a representative training subset with the largest Lyapunov exponent as an example; (2) inherent dynamics modeling via deterministic learning in the representative subset; (3) dynamics comparing between representative training patterns and a given test pattern through generating recognition errors; (4) and label assigning based on the minimal recognition error principle. The significance of this paper is that it improves the application of existing dynamical pattern recognition methods to large-scale datasets by incorporating representative selection strategies. The proposed method can achieve comparable classification accuracy on a small representative subset of chaotic trajectories, as compared to the original large-scale training set. Numerical simulations are provided to demonstrate the effectiveness of the proposed method. The simulation results show that the proposed method outperforms even the baseline deep learning methods on the representative subset in the dynamical system classification tasks. [ABSTRACT FROM AUTHOR]

Runtime verification (RV) refers to methods for formal reasoning about all aspects of the dynamic execution of systems, including hardware, software, and cyber-physical systems. RV includes techniques to assess and enforce correctness of a system against systemic bugs or extrinsic uncertainties. These methods are typically considered lightweight as they may not involve exhaustive verification or proofs, but they provide a higher level of rigor and versatility compared to conventional testing methods. This article introduces the extended versions of selected papers from the peer-reviewed proceedings of the 21st International Conference on Runtime Verification (RV 2021). RV 2021 was supposed to be held in Los Angeles, California, USA in November 2021, but was instead held virtually due to the global Covid-19 pandemic. [ABSTRACT FROM AUTHOR]

This paper uses the theory of planar dynamic systems and the knowledge of reaction-diffusion equations, and then studies the bounded traveling wave solution of the generalized Boussinesq equation affected by dissipation and the influence of dissipation on solitary waves. The dynamic system corresponding to the traveling wave solution of the equation is qualitatively analyzed in detail. The influence of the dissipation coefficient on the solution behavior of the bounded traveling wave is studied, and the critical values that can describe the magnitude of the dissipation effect are, respectively, found for the two cases of b3 < 0 and b3 > 0 in the equation. The results show that, when the dissipation effect is significant (i.e., r is greater than the critical value in a certain situation), the traveling wave solution to the generalized Boussinesq equation appears as a kink-shaped solitary wave solution; when the dissipation effect is small (i.e., r is smaller than the critical value in a certain situation), the traveling wave solution to the equation appears as the oscillation attenuation solution. By using the hypothesis undetermined method, all possible solitary wave solutions to the equation when there is no dissipation effect (i.e., r = 0) and the partial kink-shaped solitary wave solution when the dissipation effect is significant are obtained; in particular, when the dissipation effect is small, an approximate solution of the oscillation attenuation solution can be achieved. This paper is further based on the idea of the homogenization principles. By establishing an integral equation reflecting the relationship between the approximate solution of the oscillation attenuation solution and the exact solution obtained in the paper, and by investigating the asymptotic behavior of the solution at infinity, the error estimate between the approximate solution of the oscillation attenuation solution and the exact solution is obtained, which is an infinitesimal amount that decays exponentially. The influence of the dissipation coefficient on the amplitude, frequency, period, and energy of the bounded traveling wave solution of the equation is also discussed. [ABSTRACT FROM AUTHOR]

This paper presents an improved method for computing convex and concave relaxations of the parametric solutions of ordinary differential equations (ODEs). These are called state relaxations and are crucial for solving dynamic optimization problems to global optimality via branch-and-bound (B &B). The new method improves upon an existing approach known as relaxation preserving dynamics (RPD). RPD is generally considered to be among the best available methods for computing state relaxations in terms of both efficiency and accuracy. However, it requires the solution of a hybrid dynamical system, whereas other similar methods only require the solution of a simple system of ODEs. This is problematic in the context of branch-and-bound because it leads to higher cost and reduced reliability (i.e., invalid relaxations can result if hybrid mode switches are not detected numerically). Moreover, there is no known sensitivity theory for the RPD hybrid system. This makes it impossible to compute subgradients of the RPD relaxations, which are essential for efficiently solving the associated B &B lower bounding problems. To address these limitations, this paper presents a small but important modification of the RPD theory, and a corresponding modification of its numerical implementation, that crucially allows state relaxations to be computed by solving a system of ODEs rather than a hybrid system. This new RPD method is then compared to the original using two examples and shown to be more efficient, more robust, and of almost identical accuracy. [ABSTRACT FROM AUTHOR]

Due to the spectrum and complexity efficiency, the integrated radar and communications (RadCom) systems have been widely favored, in which orthogonal frequency division multiplexing (OFDM) is the most popular signal to conduct the two functions simultaneously. However, an unoptimized pulse could suffer from severe inter-carrier interference (ICI) and high out-of-band emission (OOBE), which greatly degrades the system performance. In this paper, we introduce the pulse shaping scheme dedicated to RadCom systems, in which both transmitter and receiver can adaptively design pulses with the assistance of radar estimation. We first optimize the transmitting pulse with the weighted sum of signal-to-interference-plus-noise ratio (SINR) and OOBE by employing the popular genetic algorithm. Then, we design an improved-matched pulse at the receiver for maximizing the SINR with the fmincon solver. In this way, they both utilize the readily available radar information and keep the pulse optimal even in highly dynamic scenarios, which makes the most of RadCom systems while avoiding the overhead of channel estimation and feedback. Simulations prove the feasibility of proposed scheme and reveal that the radar image and communications SINR stay close to their optimum in most cases with much lower OOBE. An improved-matched pulse can further improve the communications performance when severe ICI occurs compared with a matched pulse. [ABSTRACT FROM AUTHOR]

We investigate a competitive diffusion–advection Lotka–Volterra model with more general nonlinear boundary condition. Based on some new ideas, techniques, and the theory of the principal spectral and monotone dynamical systems, we establish the influence of the following parameters on the dynamical behavior of system (1.2): advection rates α u and α v , interspecific competition intensities c u and c v , the resources functions r u and r v of the two competitive species, and nonlinear boundary functions g 1 and g 2 . The models of (Tang and Chen in J. Differ. Equ. 269(2):1465–1483, 2020; Zhou and Zhao in J. Differ. Equ. 264:4176–4198, 2018) are particular cases of our results when g i ≡ c o n s t for i = 1 , 2 , and hence this paper extends some of the conclusions from (Tang and Chen in J. Differ. Equ. 269(2):1465–1483, 2020; Zhou and Zhao in J. Differ. Equ. 264:4176–4198, 2018). [ABSTRACT FROM AUTHOR]

In this paper, the Sprott C chaotic system is extended by a three-variable quadratic nonlinear function, which can generate two symmetric or asymmetric equilibrium points. Based on the Routh–Hurwitz criterion, the range of equilibrium stability of the system is determined. The dynamics of system are analyzed using bifurcation diagrams to obtain complex dynamical behavior of the system from period-doubling bifurcation to chaos. The hidden behavior is investigated by adjusting three parameters, and with the change of equilibrium stability, it is found that there are hidden attractors and self-excited attractors under two asymmetric equilibrium points, and only self-excited attractors under two symmetric equilibrium points. The hidden attractor of the system is verified by the cross section of attraction basins. The complexity spectrum of the system with parameter variation is calculated using the fuzzy entropy algorithm, spectral entropy (SE) algorithm, and C 0 algorithm. The system circuit is designed using Multisim software, and circuit simulation of hidden attractors and self-excited attractors are realized, consistent with MATLAB numerical simulation results. [ABSTRACT FROM AUTHOR]

In this paper, two dynamic models, recently proposed to describe the adaptive repeated choices of a boundedly rational consumer, are joined together. One considers a consumer adjusting the consumption level of a given good over time according to the observed discrepancy between expected and realized utility gain and modifies the utility function according to past consumption experience, also including saturation effects when past consumption is excessive. The other one considers the same adjustment mechanism with constant preferences but with a behavioral effect that introduces a tendency (or bias) to imitate a reference group of consumers. Merging these two models, a two-dimensional nonlinear dynamical system is obtained which describes consumers that decide their next period consumption of a given good by following two different (sometimes contrasting) criteria: their own utility maximization on the one side and imitation of a reference group of consumers on the other side. This leads to a greater uncertainty with respect to the model without the behavioral bias. Such uncertainty is studied through a numerical exploration of the long-run dynamics, guided by some global dynamical features of the nonlinear model, such as the folding action of the critical curves that characterize the behavior of the iterated noninvertible map and the singularities related to the presence of a vanishing denominator, namely focal points and prefocal curves. So, the aim of the paper is twofold: on the one side, it tries to contribute to the literature on the economic theory of boundedly rational consumers represented by evolutionary and behavioral approaches; On the other side, it tries to contribute to the recent literature about the global analysis of discrete dynamical systems characterized by contact bifurcations leading to the creation of complex topological structures of the attractors and their basins of attraction. [ABSTRACT FROM AUTHOR]

We study locally maximal attractors of expanding dynamical systems. Our main result is a representation of these attractors with the help of topological Markov chains corresponding to the Markov partitions of these attractors, which allows us to describe the dynamics of system on them. Ya. G. Sinai was the first who constructed and used Markov partitions for Anosov's diffeomorphisms [Funk. Anal. Prilozh., 2, No 1, 64; No 3, 70 (1968); English translation:Funct. Anal. Appl., 2, No 1, 61; No 3, 245 (1968)]. Expanding endomorphisms regarded as the simplest representatives of endomorphisms were first studied by M. Shub [Amer. J. Math., 91, No 1, 175 (1969)]. To construct Markov partitions for expanding endomorphisms, we update Sinai's approach in the proper way. A more detailed historical overview can be found in the work by O. M. Sharkovsky [Ukr. Mat. Zh., 74, No. 12, 1709 (2023); English translation:Ukr. Math. J., 74, No. 12, 1950 (2023)]. In this work, Sharkovsky indicated that the methods used to prove the main results presented in [Dokl. Akad. Nauk SSSR, 170, No. 6, 1276 (1966); English translation:Sov. Math. Dokl., 7, No. 5, 1384 (1966)] were, in fact, published in the collection of papers "Dynamical systems and the problems of stability of solutions of differential equations" (1973) issued by the Institute of Mathematics of the Academy of Sciences of Ukraine. This collection is difficultly accessible and was never translated into English. Note that, in the indicated paper, these methods were applied to somewhat different objects. To the best of our knowledge, there is no information about publications of similar results. In view of the outlined history and importance of the described approach (based on Markov partitions and topological Markov chains) for the description of construction of the attractors, it seems reasonable to publish these results anew. [ABSTRACT FROM AUTHOR]

This paper introduces Finite Elements with Switch Detection (FESD), a numerical discretization method for nonsmooth differential equations. We consider the Filippov convexification of these systems and a transformation into dynamic complementarity systems introduced by Stewart (Numer Math 58(1):299–328, 1990). FESD is based on solving nonlinear complementarity problems and can automatically detect nonsmooth events in time. If standard time-stepping Runge–Kutta (RK) methods are naively applied to a nonsmooth ODE, the accuracy is at best of order one. In FESD, we let the integrator step size be a degree of freedom. Additional complementarity conditions, which we call cross complementarities, enable exact switch detection, hence FESD can recover the high order accuracy that the RK methods enjoy for smooth ODE. Additional conditions called step equilibration allow the step size to change only when switches occur and thus avoid spurious degrees of freedom. Convergence results for the FESD method are derived, local uniqueness of the solution and convergence of numerical sensitivities are proven. The efficacy of FESD is demonstrated in several simulation and optimal control examples. In an optimal control problem benchmark with FESD, we achieve up to five orders of magnitude more accurate solutions than a standard time-stepping approach for the same computational time. [ABSTRACT FROM AUTHOR]

We consider systems with unboundedly many processes that communicate through shared memory. In that context, simple verification questions have a high complexity or, in the case of pushdown processes, are even undecidable. Good algorithmic properties are recovered under round-bounded verification, which restricts the system behavior to a bounded number of round-robin schedules. In this paper, we extend this approach to a game-based setting. This allows one to solve synthesis and control problems and constitutes a further step towards a theory of languages over infinite alphabets. [ABSTRACT FROM AUTHOR]

In this paper, we provide sharp criteria of global attraction for a class of non-autonomous reaction–diffusion equations with delay and Neumann conditions. Our methodology is based on a subtle combination of some dynamical system tools and the maximum principle for parabolic equations. It is worth mentioning that our results are achieved under very weak and verifiable conditions. We apply our results to a wide variety of classical models, including the non-autonomous variants of Nicholson's equation or the Mackey–Glass model. In some cases, our technique gives the optimal conditions for the global attraction. [ABSTRACT FROM AUTHOR]

Transient stability is the key aspect of power system dynamic security assessment, and data-driven methods are becoming alternative measures of assessment. The current data-driven methods only construct correlations between variables while neglecting causal relationships. Therefore, they face problems such as poor robustness, which restrict their practical application. This paper introduces an improved constraint-inference approach for causality exploration of power system transient stability. Firstly, a causal structure discovery method of power system transient stability is proposed based on a PC-IGCI algorithm, which addresses the shortage caused by Markov equivalence and massive variables. Then, a relative average causal effect index is proposed to reveal the relationship between relative intervention strength and causal effects. The results of a case study verify that the proposed method can identify the causal structure between the transient stability variables entirely based on data. In addition, the causal effect sorting between "cause" and "outcome" of transient stability variables is revealed. This paper provides a new approach for data mining to uncover the causal mechanisms between variables in power systems and expand the capabilities of data-driven methods in power system application. [ABSTRACT FROM AUTHOR]

Robust stability properties of continuous-time dynamical neural networks involving time delay parameters have been extensively studied, and many sufficient criteria for robust stability of various classes of delayed dynamical neural networks have been obtained in the past literature. The class of activation functions and the types of delay terms involved in the mathematical models of dynamical neural networks are two main parameters in the determination of stability conditions for these neural network models. In this article, we will analyse a neural network model of relatively having a more complicated mathematical form where the neural system has the multiple time delay terms and the activation functions satisfy the Lipschitz conditions. By deriving a new and alternative upper bound value for the l 2 -norm of uncertain intervalised matrices and constructing some various forms of the same type of a Lyapunov functional, this paper will first propose new results on global robust stability of dynamical Hopfield neural networks having multiple time delay terms in the presence of the Lipschitz activation functions. Then, we show that some simple modified changes in robust stability conditions proposed for multiple delayed Hopfield neural network model directly yield robust stability conditions of multiple delayed Cohen-Grossberg neural network model. We will also make a very detailed review of the previously published robust stability research results, which are basically in the nonsingular M-matrix or various algebraic inequalities forms. In particular, the robust stability results proposed in this paper are proved to generalize almost all previously reported robust stability conditions for multiple delayed neural network models. Some concluding remarks and future works regarding robust stability analysis of dynamical neural systems are addressed. [ABSTRACT FROM AUTHOR]

In this paper, interval observers are designed for linear dynamic systems described by continuous-time models with exogenous disturbances, measurement noises, and parametric uncertainties. Jordan canonical form-based relations are presented for an interval observer that estimates the set of admissible values of a given linear function of the system state vector. The theoretical results are illustrated by a practical example. [ABSTRACT FROM AUTHOR]

In the course of digitization, there is an increased interest in sensor data, including data from old systems with a service life of several decades. Since the installation of sensor technology can be quite expensive, soft sensors are often used to enhance the monitoring capabilities. Soft sensors use easy-to-measure variables to predict hard-to-measure variables, employing arbitrary models. This is particularly challenging if the observed system is complex and exhibits dynamic behavior, e.g., transient responses after changes in the system. Data-driven models are, therefore, often used. As recent studies suggest using Transformer-based models for regression tasks, this paper investigates the use of Transformer-based soft sensors for modelling the dynamic behavior of systems. To this extent, the performance of Multilayer Perceptron (MLP) and Long Short-term Memory (LSTM) models are compared to Transformers, based on two data sets featuring dynamic behavior in terms of time-delayed variables. The outcomes of this paper demonstrate that while the Transformer can map time delays, it is outperformed by MLP and LSTM. This deviation from previous Transformer evaluations is noteworthy as it may be influenced by the dynamic characteristics of the input data set, and its attention-based mechanism may not be optimized for sequential data. It is important to mention that the previous studies in this area did not focus on time-delayed dynamic variables. [ABSTRACT FROM AUTHOR]

This article investigates the phenomenon of bifurcation induced by double grazing in a piecewise-smooth oscillator with a play, which is a common occurrence in many non-smooth dynamical systems namely gear systems with approval, flange contact in wheel-rail systems, and spacecraft docking. The study is carried out using a composite Poincaré mapping with bilateral constraint, which extends the local normal form mapping of one discontinuity boundary to two discontinuity boundaries. The paper first derives the local discontinuous mapping at the unilateral grazing point using the normal form of discontinuity mapping and determines the type of 3/2 singularity of the zero-time discontinuous mapping with a continuous vector field at the discontinuity boundary. The composite Poincaré mapping is then used to obtain non-classical local bifurcations caused by double grazing, including bifurcation from period-1 motion to period-2 motion, bifurcation from period-1 motion to period-3 motion, and bifurcation from period-1 motion to chaos. The results of the study are consistent with those obtained via direct numerical simulations, demonstrating the efficacy of the composite Poincaré mapping of double grazing. The paper sheds light on the behavior of non-smooth dynamical systems and provides insights into the mechanisms underlying bifurcation induced by double grazing. The findings have potential applications in various fields including engineering, physics, and biology. [ABSTRACT FROM AUTHOR]

In this paper, delayed impulsive control for fractional-order dynamic systems via event-triggering mechanism (ETM) is investigated, in which the impact of time delays in impulses is taken into account. Combining the novel event-triggering function into the transformed fractional-order delayed impulsive control system, the event-triggered impulsive sequence is generated. Under the frame of event-based delayed impulsive control (EDIC) technique, system signals are only allowed to be transmitted at discrete instants, while no additional control input is required for two successive impulsive instants. Then, the positive quantity of inter-execution is proved, which can exclude the Zeno behavior. Furthermore, the relationship is discussed among delayed impulsive functions, event-triggering parameters, and the order of controlled fractional-order systems. Compared with traditional time-triggered mechanism where the impulsive instants are required to be set in advance, EDIC can be viewed as a more flexible impulsive control since it makes impulsive control only activate when designed events occur, effectively improving the control efficiency. The simulation results are provided to verified the effectiveness of the proposed method at the end of this paper. [ABSTRACT FROM AUTHOR]

We study the Hamilton–Jacobi equation with coinvariant derivatives corresponding to dynamical systems of the neutral type. Moreover, in contrast to the previous papers, the Hamiltonian in the equation may not satisfy the homogeneity condition. We give a definition of a minimax (generalized) solution of this equation. The existence and uniqueness of this solution is proved, and its consistency with the concept of solution in the classical sense is established. The proofs are based on the choice of a suitable Lyapunov–Krasovskii functional. [ABSTRACT FROM AUTHOR]

This paper studies the dynamic analysis, circuit implementation and circuit synchronization of a class of fractional-order memristor chaotic system based on Chua's circuit. First, the dynamic characteristics of the system was analyzed with the common chaotic description methods, such as Lyapunov exponent spectrum(LEs), bifurcation diagram, Poincaré diagram, phase trajectory diagram and Complexity spectral entropy (Complexity SE). It can be found that the small change of the initial value can make the dynamic behavior of the system change between the periodic window and the chaotic region. When fractional order q and system parameters are used as a variable, the dynamic behavior of the system can be changed. Second, the system circuit model was modeled and simulated, and then the consistency with the numerical simulation was verified through the implementation of the circuit. Finally, through the design of fractional-order memristor circuit, the circuit synchronization of the system was realized. Therefore, this paper not only studies the dynamic behavior of the system through numerical analysis. Moreover, the effectiveness of the system design is further illustrated by the implementation of analog circuit. [ABSTRACT FROM AUTHOR]

A hybrid system interacts with the discrete and continuous dynamics of a physical dynamical system. The notion of a hybrid system gives embedded control systems a great advantage. The Langevin differential equation can accurately depict many physical phenomena and help researchers effectively represent anomalous diffusion. This paper considers a fractional hybrid Langevin differential equation, including the ψ-Caputo fractional operator. Furthermore, some novel boundaries selected are considered to be a problem. We used the Schauder and Banach fixed-point theorems to prove the existence and uniqueness of solutions to the considered problem. Additionally, the Ulam-Hyer stability is evaluated. Finally, we present a representative example to verify the theoretical outcomes of our findings. [ABSTRACT FROM AUTHOR]

Nonlinear dynamical problems, characterized by unpredictable and chaotic changes among variables over time, pose unique challenges in understanding. This paper explores the coupled nonlinear (2+1)-dimensional complex modified Korteweg-de-Vries (cmKdV) equation-a fundamental equation in applied magnetism and nanophysics. The study focuses on dynamic behaviors, specifically examining bifurcations and equilibrium points leading to chaotic phenomena by introducing an external term to the system. Employing chaos theory, we showcase the chaotic tendencies of the perturbed dynamical system. Additionally, a sensitivity analysis using the Runge-Kutta method reveals the solution's stability under slight variations in initial conditions. Innovatively, the paper utilizes the planar dynamical system technique to construct various solitons within the governing model. This research provides novel insights into the behavior of the (2+1)-dimensional cmKdV equation and its applications in applied magnetism and nanophysics. [ABSTRACT FROM AUTHOR]

This paper is mainly focused on the solution of Sylvester matrix differential equations with time-independent coefficients. We propose a new approach based on the construction of a particular constant solution which allows to construct an approximate solution of the differential equation from that of the corresponding algebraic equation. Moreover, when the matrix coefficients of the differential equation are large, we combine the constant solution approach with Krylov subspace methods for obtaining an approximate solution of the Sylvester algebraic equation, and thus form an approximate solution of the large-scale Sylvester matrix differential equation. We establish some theoretical results including error estimates and convergence as well as relations between the residuals of the differential and its corresponding algebraic Sylvester matrix equation. We also give explicit benchmark formulas for the solution of the differential equation. To illustrate the efficiency of the proposed approach, we perform numerous numerical tests and make various comparisons with other methods for solving Sylvester matrix differential equations. [ABSTRACT FROM AUTHOR]

System design is a challenging and time-consuming task which often requires close collaboration between several multidisciplinary design teams to account for complex interactions between components and sub-systems. As such, there is a growing demand in industry to create better performing, efficient, and cost-effective development tools to assist in the system design process. Additionally, the ever-increasing complexity of systems today often necessitates a shift away from manual expertise and a movement towards computer-aided design tools. This work narrows the scope of the system design process by focusing on one critical design aspect: the packaging of system components. The algorithm presented in this paper was developed to optimize the packaging of system components with consideration of practical, system-level functionalities and constraints. Using a dynamic acceleration methodology, the algorithm packages components from an initial position to a final packed position inside of a constrained volume. The motion of components from initial to final positions is driven by several acceleration forces imposed on each component. These accelerations are based on physical interactions between components and their surrounding environment. Various system-level performance metrics such as center of mass alignment and rotational inertia reduction are also considered throughout optimization. Results of several numerical case studies are also presented to demonstrate the functionality and capability of the proposed packaging algorithm. These studies include packaging problems with known optimal solutions to verify the efficacy of the algorithm. Finally, the proposed algorithm was used in a more practical study for the packaging of an urban air mobility nacelle to demonstrate the algorithm's prospective capabilities in solving real-world packaging problems. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of a reservoir that has a finite-dimensional output and makes the reservoir computing model universal. Reservoir computing is a method for dynamical system approximation that trains the static part of a model but fixes the dynamical part called the reservoir. Hence, reservoir computing has the advantage of training models with a low computational cost. Moreover, fixed reservoirs can be implemented as physical systems. Such reservoirs have attracted attention in terms of computation speed and energy consumption. The universality of a reservoir computing model is its ability to approximate an arbitrary system with arbitrary accuracy. Two sufficient reservoir conditions to make the model universal have been proposed. The first is the combination of fading memory and the separation property. The second is the neighborhood separation property, which we proposed recently. To date, it has been unknown whether a reservoir with a finite-dimensional output can satisfy these conditions. In this study, we prove that no reservoir with a finite-dimensional output satisfies the former condition. By contrast, we propose a single output reservoir that satisfies the latter condition. This implies that, for any dimension, a reservoir making the model universal exists with the output of that specified dimension. These results clarify the practical importance of our proposed conditions. [ABSTRACT FROM AUTHOR]

In order to realize the coordinated design of multiple flexible AC transmission systems (FACTS) devices in the wind–PV–thermal-bundled (WPTB) power transmission system to suppress the low-frequency oscillation (LFO) of the system, in this paper, the static synchronous compensator (STATCOM) and the static synchronous series compensator (SSSC) with additional power oscillation damping controller (PODC) are designed based on the tie line transmission power signal to enhance the improvement effect of FACTS devices on system stability. The objective function is constructed by considering the transient voltage stability of the WPTB power transmission system, the real part of the eigenvalues and damping level of the LFO modes. And the coordinated and optimized design of power system stabilizer (PSS), SSSC-PODC and STATCOM-PODC is performed by the hybrid particle swarm optimization algorithm and genetic algorithm (PSO-GA) and pattern analysis theory of LFO. Finally, it is verified that the design can give full play to the effect of different controllers and significantly improve the damping ratio of the oscillation mode between regions through the simulation under the output variation of the new energy unit and the transmission power variation of the liaison line. When the fault occurs, the amplitude of oscillation and the time required to recover stability of the system decrease obviously, which enhances the dynamic stability of the system. [ABSTRACT FROM AUTHOR]

Modern measurement systems have allowed the recording of ambient data containing oscillatory phenomena and high noise levels. The observed phenomena are associated with ambient oscillations, which can be identified for monitoring the power system's dynamic behavior. Therefore, a cross-correlation decomposition-based approach is proposed in this paper. This technique combines an extended natural excitation technique (ENEXT) with a parallel factor (PARAFAC) analysis. The ENEXT allows calculating correlation functions of the measured data, which can be employed to build a data tensor. From this data array, a set of dominant impulse responses and their spatial correlations can be extracted through the PARAFAC analysis. The cross-correlation decomposition-based approach is applied to ambient data from the IEEE 16-generator 5-area power system to characterize dominant inter-area oscillation modes. The results demonstrate that the impulse responses may be used to identify the modal parameters, and the spatial correlations may be used to identify the spatial distribution of the oscillatory modes. [ABSTRACT FROM AUTHOR]

In this paper we give a complete characterization of those knotted toroidal sets that can be realized as attractors for discrete or continuous dynamical systems globally defined in R 3 . We also see that the techniques used to solve this problem can be used to give sufficient conditions to ensure that a wide class of subcompacta of R 3 that are attractors for homeomorphisms must also be attractors for flows. In addition we study certain attractor-repeller decompositions of S 3 which arise naturally when considering toroidal sets. [ABSTRACT FROM AUTHOR]