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We study the existence and uniqueness of solutions to the inverse quasi-variational inequality problem. Motivated by the dynamical approach to solving optimization problems such as variational inequality, monotone inclusion, and inverse variational problems, we consider a dynamical system associated with the inverse quasi-variational inequality problem, and establish the existence and uniqueness of a solution to the proposed system. We prove that every trajectory of the proposed dynamical system converges to the unique solution of the inverse quasi-variational inequality problem and that the system is globally asymptotically stable at its equilibrium point. We also prove that if the function which governs the inverse quasi-variational inequality problem is strongly monotone and Lipschitz continuous, then the dynamical system is globally exponentially stable at its equilibrium point. We discretize the dynamical system and show that the sequence generated by the discretization of the system converges strongly to the unique solution of the inverse quasi-variational inequality problem under certain assumptions on the parameters involved. Finally, we provide numerical examples to support and illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

Let $ (X, f) $ (X , f) be a dynamical system, i.e. X is a compact metric space and f is a continuous self-map on X and let $ K(X) $ K (X) , $ M(X) $ M (X) and $ \mathbb {F}(X) $ F (X) be the sets of all non-empty compact subsets of X, Borel probability measures on X and upper semi-continuous fuzzy sets on X, respectively. Then $ K(X) $ K (X) , $ M(X) $ M (X) and $ \mathbb {F}(X) $ F (X) are metric spaces under Hausdorff metric, prohorov metric and level-wise metric, respectively. Therefore, $ (X, f) $ (X , f) naturally induces three new systems $ (K(X), \bar {f}) $ (K (X) , f ¯) , $ (M(X), \hat {f}) $ (M (X) , f ^) and $ (\mathbb {F}(X), \tilde {f}) $ (F (X) , f ~). In this article, we investigate the connection of $ (r,s) $ (r , s) -sensitivity, $ (r,s) $ (r , s) -asymptotic sensitivity, $ (r,s) $ (r , s) -Li-Yorke sensitivity and Δ-transitivity of $ (X, f) $ (X , f) and its induced systems $ (K(X),\bar {f}) $ (K (X) , f ¯) , $ (M(X),\hat {f}) $ (M (X) , f ^) and $ (\mathbb {F}(X),\tilde {f}) $ (F (X) , f ~) and we obtain some desired results. For instance, we prove that $ (K(X),\bar {f}) $ (K (X) , f ¯) is $ (r,s) $ (r , s) -sensitive ⇔ $ (\mathbb {F}^{1}(X),\widetilde {f_{g}}) $ (F 1 (X) , f g ~) is $ (r,s) $ (r , s) -sensitive for each $ g\in D_{m}(I) $ g ∈ D m (I) satisfying $ g^{-1}(1)=\{1\} $ g − 1 (1) = { 1 } ; $ (X,f) $ (X , f) is Δ-transitive ⇔ $ (K(X),\bar {f}) $ (K (X) , f ¯) is Δ-transitive ⇔ $ (M(X),\hat {f}) $ (M (X) , f ^) is Δ-transitive $ \Leftrightarrow \,(\mathbb {F}^{1}(X),\tilde {f}) $ ⇔ (F 1 (X) , f ~) is Δ-transitive. [ABSTRACT FROM AUTHOR]

Process control is widely discussed in the manufacturing process, especially in semiconductor manufacturing. Due to unavoidable disturbances in manufacturing, different process controllers are proposed to realize variation reduction. Since Reinforcement Learning (RL) has shown great advantages in learning actions from interactions with a dynamic system, we introduce RL methods for process control and propose a new controller called RL-based controller. Considering the fact that most existing run-to-run (R2R) controllers mainly rely on a linear model assumption for the process input–output relationship, we first discuss theoretical properties of RL-based controllers based on the linear model assumption. Then the performance of RL-based controllers and traditional R2R controllers (e.g., Exponentially Weighted Moving Average (EWMA), double EWMA, adaptive EWMA, and general harmonic rule controllers) are compared for linear processes. Furthermore, we find that the RL-based controllers have potential advantages to deal with other complicated nonlinear processes. The intensive numerical studies validate the advantages of the proposed RL-based controllers. [ABSTRACT FROM AUTHOR]

This paper is devoted to the stochastic travelling wave solutions of a three-species competitive–cooperative system with multiplicative noise. The existence of the travelling wave solutions can be proved by constructing upper/lower-solution and stochastic dynamical systems theory. Moreover, under the more restricted assumption on the coefficients of system, and applying Feynman–Kac formula and upper/lower solution technique, the upper/lower bounds of the asymptotic wave speed can be provided. [ABSTRACT FROM AUTHOR]

We develop the theory of kernel sections of non-autonomous dynamical systems. Under some sufficient conditions, we establish some abstract results on the asymptotically autonomous stability of kernel sections, which suggests that the time-section of a kernel section is asymptotically stable to a global attractor of the autonomous dynamical system. A lattice plate equation with nonlinear damping and non-autonomous forcing is considered as an application. It is shown that the time-section of kernel sections of the non-autonomous lattice plate equations are nonempty, uniformly compact, pullback attracting, and asymptotically stable to a global attractor of the autonomous lattice plate equations. [ABSTRACT FROM AUTHOR]

In this paper, we study some Krasnoselskii-Mann type dynamical systems in solving fixed point problems. The first one can be regarded as a continuous version of the Krasnoselskii-Mann iterations. We prove that the solution of this dynamical system converges weakly to a fixed point of the involving mapping. Next, we focus our attention on a regularized Krasnoselskii-Mann type dynamical system. Besides proving existence and uniqueness of strong global solutions, we show that the generated trajectories converge strongly to a unique solution of a variational inequality over the fixed point set. Also, we provide a convergence rate analysis for the regularized dynamical system. [ABSTRACT FROM AUTHOR]

Partially stable systems involve dynamical systems whose motion lie in a subspace of the state space resulting in system stability with respect to part of the system's states. In this paper, we develop partial stability theorems for nonlinear continuous-time and discrete-time dissipative feedback systems. Specifically, by invoking additional structural constraints on the forward loop and feedback loop system storage functions, we develop feedback interconnection partial stability results for dissipative nonlinear dynamical systems. Our results provide extensions of the positivity and small gain theorems for guaranteeing partial stability of feedback interconnected systems. [ABSTRACT FROM AUTHOR]

The axle box bearing serves as a critical rotational component for high-speed trains. Thus, it is of great significance to obtain accurate loading conditions for axle box bearings for its reliability design. In this study, a bearing-vehicle coupled system dynamic model, consisting of an equivalent bearing model characterized by the time-varying stiffness in the bearing, a nonlinear high-speed train dynamic model, and a slab track model, is developed. The validity of the proposed coupled dynamic model is demonstrated by comparing the simulated results with those obtained in a field test and the literature, respectively. Subsequently, the influence of long- and short-wavelength irregularities on the dynamic responses of bearings is investigated using the proposed coupled model in terms of dynamic loads of the axle box bearing. The results obtained by the proposed model are further compared with those calculated using a traditional vehicle dynamic model that represents the bearing as a revolute joint, so as to illustrate the advantages of the proposed model. The results suggest that the loading responses of the bearing calculated by the two models exhibit differences, which are simultaneously related to the structural damping of the bearing and the mode frequency change of the system. [ABSTRACT FROM AUTHOR]

In this research article, the dynamics of optical solitons in cascaded system with spatio-temporal dispersion is discussed. The Kerr medium is considered for this investigation. Two versatile integration tools have been used to extricate different traveling wave solutions. Rapid convergent approximation method has been employed to extract bright, singular and periodic solitons whereas polynomial function solutions are obtained by unified method. The constraints on the parameters for the validity of these solutions are also provided. Galilean transformation is prosecuted to construct the planer dynamical system of the said model. Runge–Kutta fourth-order technique is used to extract the non-linear periodic waves of the considered problem and consequences are depicted through different portraits. Further, by employing an extrinsic periodic force, chaotic and quasiperiodic pattern of discussed model is analyzed for different values of the parameters. While chaotic and quasiperiodic behaviors are observed for some values of parameters of considered system by keeping the force and frequency of the perturbed dynamical system fixed. Sensitive anatomy is carried out for diverse initial value problems. It is investigated that the chaotic and quasiperiodic pattern is present in the perturbed dynamical system. [ABSTRACT FROM AUTHOR]

In this study, control and fault detection are examined for Takagi–Sugeno (T–S) fuzzy continuous-time systems with conic-type nonlinearity. In a conic-type dynamic system, Takagi–Sugeno fuzzy models are applied. A conic-type non-linearity must lie in an n-dimensional hyper-sphere with an uncertain centre to satisfy the restrictive condition. A combined error system of estimation and control error is obtained by combining the observations and the controller. Our main goal is to design an observer and controller for fault detection that minimizes the impact of unknown inputs and faults on the system in terms of the $ H_{\infty } $ H ∞ performance. The Lyapunov function is used to construct the residual signal using an observer and a controller. Using Linear Matrix Inequalities (LMIs), we can express the performance conditions for $ H_{\infty } $ H ∞ . The scheme's effectiveness is demonstrated with numerical examples. [ABSTRACT FROM AUTHOR]

We study the metric mean dimension of Φ-irregular set $ I_{\Phi }(f) $ I Φ (f) in dynamical systems with the shadowing property. In particular, we prove that for dynamical systems with the shadowing property containing a chain recurrent class Y, the values of topological entropy together with the values of lower and upper metric mean dimension of the set $ I_{\Phi }(f)\cap B(Y,\varepsilon)\cap CR(f) $ I Φ (f) ∩ B (Y , ε) ∩ CR (f) are bounded from below by the respective values for class Y. [ABSTRACT FROM AUTHOR]

In the following article, we construct an interaction model of general language change. This contributes in particular to quantitative studies on reversible language change initiated by G. Altmann by adding explanatory character in tracing global features of general language change back to the individual interaction of speakers. Although the corresponding coupled differential equations are (presumably) non-integrable, we use methods from the theory of dynamical systems to deduce the long-term behaviour (depending on four interaction parameters) of the model for any given initial constellation of speakers. Subsequent numerical analysis of real data on language change is used to justify the relevance of the constructed model for the practicing quantitative linguist. We show how data-fitting methods can be used to determine the four interaction parameters and predict from them the long-term behaviour of the system, i.e. if complete language change or reversible language change will take place. [ABSTRACT FROM AUTHOR]

This paper proposes a user-biometric-based image encryption using chaotic dynamical systems, SHA-256 hash function, and zigzag transformation. Three chaotic systems, namely, the Henon map, logistic map, and Lorenz system, are used to apply the chaotic properties to the encryption system. The hash value of the user biometric image is used to generate the initial value of the Henon map. The initial values for the logistic map and Lorenz system are generated from the hash value of the plain image. SHA-256 hash algorithm generates the hash values of the biometric and plain images. The plain image is scrambled using the two-dimensional chaotic values generated by the Henon map first. Next, the first scrambled image's pixels are XORed with the one-dimensional chaotic values generated from the logistic map and produce the second scrambled image. Finally, take the second scrambled image's pixels, and XOR them with the three-dimensional chaotic values generated from the Lorenz system and create the final encrypted image. The robustness and flexibility of the encryption system are analyzed using various security and performance analyses. The experiment results are compared with the existing algorithms to prove the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Aiming at the nonlinear vibration problem caused by the dynamic misalignment of rolling bearings in the rotating machinery, a rotor dynamic model with bearing dynamic misalignment is established, and the effects of the dynamic misalignment of single and two bearings and the phase relationship of two dynamic misalignment bearings on the rotor vibration characteristics are researched. The effects of bearing clearance, raceway curvature radius, the ball number and radial load on the nonlinear vibration response of the dynamic misalignment bearing-unbalance rotor system are further analyzed. The results show that the dynamic misalignment of the bearing can excite the vibration at twice the rotor frequency, raise the resonance speed and enhance the hardening-type nonlinearity characteristics of the rotor. The influence of dynamic misalignment under two bearings with out-of-phase on rotor resonance is greater than that of the in-phase. The stability of the system can be improved by decreasing the bearing clearance and increasing the curvature radius coefficient. The vibration caused by bearing dynamic misalignment can be reduced by selecting the bearing with more balls and appropriately increasing the bearing load. [ABSTRACT FROM AUTHOR]

This article is concerned with the stability and stabilisation of switched time-delay systems (STDSs) with exponential uncertainty. Based on the Hurwitz convex combination and the energy attenuation principle, an improved state-dependent switching strategy is proposed, which switches to the next modes to obey the minimum energy. This approach fully considers the system dynamic of subsystems, which is more general. Considering the complex switching and delay dynamics, a mode-dependent Lyapunov–Krasovskii functional (LKF) that contains a triple integral term is constructed. The generalised free-matrix-based integral inequality (GFMBII) is used to estimate the integral terms in the derivative of the LKF, and an improved delay-dependent stability criterion is established in the form of linear matrix inequalities (LMIs). Further, to guarantee the stability of the STDSs with a large time-varying delay, a controller that considers the time delay and the exponential uncertainty is designed. Under this controller, a less conservative delay-dependent robust stabilisation criterion for STDSs with exponential uncertainty is established. The validity of the proposed methods is validated by two numerical examples and an application in river pollution control. [ABSTRACT FROM AUTHOR]

In this paper we prove several turnpike results for trajectories of discrete disperse dynamical systems introduced in 1980 by A. M. Rubinov, which have a prototype in mathematical economics. [ABSTRACT FROM AUTHOR]

Student-generated questions are an important mechanism for learning and self-regulation, yet their scarcity in classroom discourse points to a need to understand how students decide to ask or withhold their questions. This study examined how 12 graduate students in an introductory statistics course made decisions about asking questions during whole group instruction. Help seeking decisions were framed as arising from a dynamic system of a student's situated role identity as a class participant. Qualitative analysis of post-class interviews illustrated the highly contextual, dynamic nature of students' decisions to ask or withhold questions. Analyses revealed an array of microdecisions that involved determining whether help was needed, anticipating social impressions, and considering impacts on others. Results revealed a prominent configuration of ontological beliefs, self-perceptions, goals, and perceived action possibilities that led students to withhold questions. The findings highlight tensions and dynamics among role identity elements, including distinct appraisals of one's own vs. classmates' questions. The study illuminates how context, questions, and interacting identity elements frame students' willingness to ask questions during class. [ABSTRACT FROM AUTHOR]

This paper is concerned with reset controller design and $ \mathcal {L}_2 $ L 2 -gain stability of piecewise-affine systems under the framework of hybrid systems. Firstly, stability conditions of piecewise-affine systems under dynamic state-feedback control are established through bilinear matrix inequality conditions. Secondly, a reset controller with reset rules under the hybrid systems framework is proposed in the sense of Lyapunov and sufficient conditions for exponential and $ \mathcal {L}_2 $ L 2 -gain stability of the closed-loop systems are provided. Different from the piecewise-affine systems with the dynamic state-feedback controller, the reset controller is designed such that the $ \mathcal {L}_2 $ L 2 -gain performance of piecewise-affine systems can be enhanced. Thirdly, an LMI approach is proposed to avoid the difficulty of solving the bilinear matrix inequalities. Furthermore, robustness to inflations of the flow and jump sets is established, and robustness to the norm-bounded uncertainties is proposed. Finally, numerical simulations including a robot arm system, an inverted pendulum system and the Chua's circuit system are provided to illustrate the results. [ABSTRACT FROM AUTHOR]

To study the evolution of the pantograph-catenary system dynamic under crosswind environments, this paper examines the effect of crosswind on the quality of the current collection and explores the wind stability of different longitudinal suspension forms of the catenary system. Firstly, the catenary with different longitudinal suspension forms is established based on the absolute node coordinate formulation, and the initial equilibrium configuration are accurately obtained. Secondly, the pantograph model is derived, and the pantograph-catenary system coupling model is established according to the standard EN 50318:2018 and passed the verification. Then, the random wind speed spectrum of the simulated environment is built based on the Davenport spectrum and is validated. Finally, the pantograph-catenary system dynamic behavior under the crosswind environments is simulated. The results show that the crosswind affects the low-frequency vibration part of the pantograph-catenary system, with the increase in wind speed and the standard deviation of contact force, the worse current collection quality. Different longitudinal suspension forms of catenary systems have various wind stability. Semi-inclined and inclined longitudinal suspension forms have better wind stability, and the maximum reduction of contact force standard deviation is 14.05%, which can effectively improve the current collection quality in crosswind environments. [ABSTRACT FROM AUTHOR]

This research tries to stabilise a three degree-of-freedom series-type double inverted pendulum system by employing an adaptive state feedback control approach optimised by a particle swarm optimisation (PSO) algorithm. To this end, the dynamical equations are derived via Lagrangian method and linearised by utilising approximation approaches. Then, the state feedback scheme is implemented to control the system states, that is, the angle and angular velocity of the first and second poles as well as the position and velocity of the cart. In order to timely regulate the control gains, the adaptation rules based on the gradient descent method and sliding surface relations are applied. The particle swarm optimisation algorithm is implemented to optimally tune the design parameters of the controller based on a proper objective function defined as summation of integrals of absolute values of the system errors. The time responses of the angles of the poles and the position of the cart clearly depict the feasibility and efficiency of the introduced control strategy to stabilise the system from different initial conditions to the final desired values. [ABSTRACT FROM AUTHOR]

One of the most widely used linear techniques for solving damage identification problems and prediction of the system dynamic behavior is modal testing and analysis. However, most of real structures exhibit nonlinear behavior during their lifetime caused by a number of various reasons. The presence of nonlinearity in a structural system changes its dynamic characteristics; hence, the use of linear techniques is improper for prediction of the system behavior. In this paper, a vibration-based nonlinearity identification technique was proposed to identify early changes in a dynamic system prior to significant damages. This technique combines the time series Autoregressive Moving Average with Exogenous Inputs (ARMAX) modelling, probability theory, and Fuzzy C-Means (FCM) clustering algorithm to categorize the linear and nonlinear dynamic behaviors of a dynamic system. The technique aims to categorize the linear and nonlinear behaviors of a structure, when it is subjected to various levels of excitation source. To show the validity of the proposed method, a series of shake table tests was performed on a six-span steel truss bridge model. The bridge model was excited using different amplitudes of ground motion to control the nonlinearity degree of rubber-based supports. It can be concluded from the analysis results that the new vibration-based nonlinearity identification technique was able to identify nonlinear behavior of the bridge model once it was subjected to different levels of earthquake excitations. This algorithm was able to categorize the linear and nonlinear behaviors of the bridge model and define a specific threshold for different excitation sources. [ABSTRACT FROM AUTHOR]

Due to high utility of the sandwich structures in the vast spectrum of applications, this research focuses on the practical solution to protect them from damaging consequences of thermal shocks through parametric assessment of its time-variant thermoelastic performance. To this end, current research proposes a novel approach by taking the advantage of coupling the exactitude of the analytical solutions with the agility of the machine-learning methods to predict the accurate results by lower computational efforts. Case study of this research is a sandwich sector plate with functionally-graded carbon-nanotubes reinforced (FG-CNTR) nanocomposite face-layers exposed to the thermal shock loading. As another novelty, this study considers a radial-variant elastic substrate as a mechanism of resistance against the destructive consequences of thermal shock loading. As all machine-learning based regressors require the set of datapoints, this study employs harmonic format of the differential quadrature approach (HDQA) to find the system's response toward thermal shock in the background of general elasticity theory at definite design- points. Laplace transform integrated with the extended model of Dubner and Abate's scheme to translate the time-variant response of the system from time to Laplace domain and vice versa. Validity of the solution used in this survey is confirmed through comparing its outcomes with those of the published articles. As a valuable finding, it is strongly suggested to enhance the system's thermal shock resistance by using the substrates which their reaction's dependency to the radial coordinate is expressed by higher-order polynomial estimator functions. [ABSTRACT FROM AUTHOR]

This article analyzes the forced and free vibrations of bi-directional functionally graded (BDFG) porous nanobeams under moving loads by considering the thickness effect based on the nonlocal strain gradient theory (NSGT). It is assumed that the material properties of the system are graded across the transverse and axial directions according to power and exponential laws, respectively. Various porosity models, including even, uneven, and asymmetric porosity distribution patterns, are considered to model the porosity effects. The dynamic equation of the system is derived by implementing the physical neutral surface concept. Analytical and numerical approaches are adopted to acquire the vibration response of the system. Mathematical closed-form expressions are provided for various dynamic phenomena, such as two types of cancelation, two types of resonance, maximum resonance, cancelation disappearance, and resonance disappearance. In addition, for the first time in this article, it is demonstrated that BDFG porous nanobeams under moving loads are prone to experience the double cancelation phenomenon. Several comparison studies with published data are conducted to validate the results. Also, comprehensive parametric studies are carried out to elucidate the impacts of system parameters such as thickness power index, axial gradient parameter, scale parameter ratio, axial force, porosity coefficient, and porosity distribution pattern on the dynamic magnification factor, critical load speed, and maximum free-response. The outcomes established that by considering the thickness effect, the stiffening behavior of the system is amplified depending on the slenderness ratio. Also, it is concluded that, among the considered porous models, the critical load speed for the system with an even porosity distribution is more dependent on the thickness power index. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive cooperative formation controller is developed to force a swarm of nonholonomic mobile robots with limited sensing ranges to move along the desired reference trajectory in a predetermined formation, while maintaining communication connectivity among the initial user-specified connected robots and guaranteeing no collision between the robots. Both kinematic models and dynamic systems with parametric uncertainties are discussed. The presence of parametric uncertainties is handled by adaptive control technique. A novel artificial potential function, which is based on a 4 times differential pseudo bump function, is constructed to achieve collision avoidance and connectivity maintenance. The control design is based on a fusion of potential function, adaptive backstepping technique, and Lyapunov synthesis. The cooperative formation controller is proven to be stable and can guarantee that there is no collision between any robots and the initial connectivity of the communication network can be always maintained. The proposed formation control approach is decentralized in the sense that the control action on each robot depends only on information from its neighbours and the desired trajectory of the group. Comparative simulation and experiment studies are performed to show the effectiveness of the proposed formation controller. [ABSTRACT FROM AUTHOR]

Dynamic systems theory and complexity theory (DST/CT) is a framework explaining how complex systems change and adapt over time. In psychotherapy, DST/CT can be used to understand how a person's mental and emotional state changes during therapy incorporating higher levels of complexity. This study aimed to systematically review the variability of DST/CT methods applied in psychotherapy research. A primary studies search was conducted in the EBSCO and Web of Knowledge databases, extracting information about the analyzed DST/CT phenomena, employed mathematical methods to investigate these phenomena, descriptions of specified dynamic models, psychotherapy phenomena, and other information regarding studies with empirical data (e.g., measurement granularity). After screening 38,216 abstracts and 4,194 full texts, N = 41 studies published from 1990 to 2021 were identified. The employed methods typically included measures of dynamic complexity or chaoticity. Computational and simulation studies most often employed first-order ordinary differential equations and typically focused on describing the time evolution of client-therapist dyadic influences. Eligible studies with empirical data were usually based on case studies and focused on data with high time intensity of within-session dynamics. This review provides a descriptive synthesis of the current state of the proliferation of DST/CT methods in the psychotherapy research field. [ABSTRACT FROM AUTHOR]

We re-consider Schelling's (1971) bounded neighborhood model as put into the form of a dynamical system by Haw and Hogan (2018). The aim is to determine how tolerance can prevent (or lead to) segregation. In the case of a single neighborhood, we explain the occurring bifurcation set, thereby correcting a scaling error. In the case of two neighborhoods, we correct a major error and derive a dynamical system that does satisfy the modeling assumptions made by Haw and Hogan (2020), staying as close as possible to their construction. We find that stable integration is then only possible if the populations in the two neighborhoods have the option to be in neither neighborhood. In the absence of direct movement between the neighborhoods, the problem is furthermore equivalent to independent single neighborhood problems. [ABSTRACT FROM AUTHOR]

In a Hilbert space setting $ {\mathcal H} $ H , for convex optimization, we analyse the fast convergence properties as $ t \rightarrow +\infty $ t → + ∞ of the trajectories $ t \mapsto u(t) \in {\mathcal H} $ t ↦ u (t) ∈ H generated by a third-order in time evolution system. The function $ f: {\mathcal H} \to {\mathbb R} $ f : H → R to minimize is supposed to be convex, continuously differentiable, with $ {\rm argmin}_{{\mathcal H}} f \neq \emptyset $ argmin H f ≠ ∅. It enters into the dynamic through its gradient. Based on this new dynamical system, we improve the results obtained by Attouch et al. [Fast convex optimization via a third-order in time evolution equation. Optimization. 2020;71(5):1275–1304]. As a main result, when the damping parameter α satisfies $ \alpha \gt 3 $ α > 3 , we show that $ f(u(t)) - \inf _{{\mathcal H}} f = o(1/t^3) $ f (u (t)) − inf H f = o (1 / t 3) as $ t \rightarrow +\infty $ t → + ∞ , as well as the convergence of the trajectories. We complement these results by introducing into the dynamic an Hessian-driven damping term, which reduces the oscillations. In the case of a strongly convex function f, we show an autonomous evolution system of the third-order in time with an exponential rate of convergence. All these results have natural extensions to the case of a convex lower semicontinuous function $ f: {\mathcal H} \to \mathbb R\cup \{+\infty \} $ f : H → R ∪ { + ∞ }. Just replace f with its Moreau envelope. [ABSTRACT FROM AUTHOR]

The photocatalytic degradation process of sulfamethoxazole (SMX) using ZnO in aquatic systems has been systematically studied by varying initial SMX concentration from 0 to 15 mgL−1, ZnO dosage from 0 to 4 gL−1 and UV light intensity at the light source from 0 to 18 W(m-lamp length)−1 at natural pH. Almost complete degradations of SMX were achieved within 120 min for the initial SMX concentration ≤15 mgL−1 with ZnO dosage of 3 gL−1 and UV light intensity of 18 W(m-lamp length)−1. The photocatalytic degradation process was found to be interacted with the dissolved oxygen (DO) consumption. With oxygen supply through the gas-liquid free-surface, the DO concentration decreased significantly in the initial SMX degradation phase and increased asymptotically to the saturated DO concentration after achieving about 80% SMX degradation. The change in DO concentration was probably controlled by the oxygen consumption in the formation of oxygenated radical intermediates. A novel dynamic kinetic model based on the fundamental reactions of photocatalysis and the formation of oxygenated radical intermediates was developed. In the modeling the dynamic concentration profiles of OH radical and DO are considered. The dynamics of SMX degradation process by ZnO was simulated reasonably by the proposed model. [ABSTRACT FROM AUTHOR]

We build a smooth real potential V(t, x) on (t 0 , + ∞) × R 2 decaying to zero as t → ∞ and a smooth solution to the associated perturbed cubic noninear harmonic oscillator whose Sobolev norms blow up logarithmically as t → ∞ . Adapting the method of Faou and Raphael for the linear case, we modulate the Solitons associated to the nonlinear harmonic oscillator by time-dependent parameters solving a quasi-Hamiltonian dynamical system whose action grows up logarithmically, thus yielding logarithmic growth for the Sobolev norm of the solution. [ABSTRACT FROM AUTHOR]

A new disintegrated channelization approach for the backward pumped nonlinear distributed Raman amplifier is proposed by enacting the differential coupled equations of Raman amplification, in fiber, trailing by the solution of NLSE using the first integral method first time to the best of our knowledge. A nonlinear channel modeling-based simulation is adapted for the approximation of the Raman gain profile. To realize the real-time dynamic system, 16 multiplexed channels of prime C-band are employed in a QPSK/NRZ modulation environment with a 100 Gbps bit rate for optical network reconfiguration. A non-uniform gain is reported while the disparity in BER is observed from 10−12 to 10−8. [ABSTRACT FROM AUTHOR]

In this article, we formulate and investigate dynamic optimisation of systems with control limits. Aerial, electronic, electromechanical, mechatronic and robotic systems exhibit symmetric and asymmetric bounds. Applying a Hamiltonian optimisation, and, minimisation of specified-by-constraints nonquadratic performance functionals result in analytically designed bounded control laws. Closed form solution of an optimisation problem is found. Continuous control algorithms ensure consistency to physical systems and homogeneous performance. Findings in dynamic optimisation and constrained control are analytically, numerically and experimentally substantiated. Experimental studies and results are documented for a dc-dc switching regulator and permanent-magnet synchronous motor. [ABSTRACT FROM AUTHOR]

The effect of a double-layer slit-type distributor with dynamically adjustable opening porosity on the fluidized drying of Geldart D particles was investigated. The Ergun equation parameters were corrected for the fluidization equipment and material to accurately predict the pressure drop when the slit distribution plate starts fluidizing the green beans. In this study, the bed pressure drop and distributor opening porosity during fluidization were regression fitted to the dry basis moisture content of the material, and a method to determine the drying stage based on the regression fitting equation was proposed. The dynamic adjustment system of distributor opening porosity was established for the research results, and the application test found that the system can effectively improve the drying efficiency of material fluidization and reduce the abnormal fluidization phenomenon. [ABSTRACT FROM AUTHOR]

Under the sharp turn condition, especially on low adhesion coefficient roads, drift motion can improve vehicle agility and ensure safety. During drift motion, the large sideslip angle and rear wheel slip as well as the saturation of lateral tyre force result in the complex nonlinear dynamic behaviour, such as non-unique equilibrium point and unstable vehicle dynamic. Therefore, this paper focuses on the analysis of dynamic characteristics and the design of both the equilibrium point and feedback controller for drift motion. First, a dynamics model, in which the rear wheel slip ratio is treated as a parametric variable and the influence of rear wheel lateral force on the drift motion is explicitly expressed, is established. Then the expression of steady-state yaw rate and the virtual control input is derived, and the error dynamic model is presented furthermore. To design the equilibrium point, in this paper the effect of rear tyre slip angle and slip ratio on the equilibrium point is discussed, and the condition of stable equilibrium point is proposed. In addition, the design of desired rear tyre slip angle by synthesising the cornering performance during drift motion is presented. For the drift controller design, the main idea is to design the stabilisation controller for the nonlinear dynamic system with the stable equilibrium point and to calculate static feedback gain by means of Lyapunov stability theory. To illustrate the characteristics of drift motion, the influence of the vehicle speed and rear wheel slip ratio on the vehicle path and the low damping characteristics of the dynamic system on the control performance are analysed by different simulation conditions. Moreover, the performance and effectiveness of the proposed drift control are verified by simulation. [ABSTRACT FROM AUTHOR]

AbstractIntroductionMethodResultsConclusionsFlexibility, the ability of an individual to adapt to environmental changes in ways that facilitate goal attainment, has been proposed as a potential mechanism underlying psychopathology and psychotherapy. In psychotherapy, most findings are based on self-report measures that have important limitations. We propose a multimodal, multi-dyad approach based on a nonlinear dynamical systems framework to capture the complexity of this concept.A new research paradigm was designed to explore the validity of the proposed conceptual model. The paradigm includes a psychotherapy-like social interaction, during which body movement and facial expressiveness data were collected. We analyzed the data using Hankel Alternative View of Koopmann analysis to reconstruct attractors of the observed behaviors and compare them.The patterns of behavior in the two cases differ, and differences in the reconstructed attractors correspond with differences in self-report measures and behavior in the interactions.The case studies show that information provided by a single modality is not enough to provide the full picture, and multiple modalities are needed. These observations can serve as an initial support for our claims that a multi-modal and multi-dyad approach to flexibility can address some of the issues of measurement in the field. [ABSTRACT FROM AUTHOR]

The present paper proposes a novel disturbance rejection-based scheme applied to a power system for concurrent control of system voltage, frequency, and tie-line power. The generating units in the power system comprise varied generating sources, such as thermal, diesel, solar-thermal, and wind sources. Owing to the present rigid limitations on energy assets and environmental alarms, electric vehicles are integrated with the power system in both areas. The complex power system needs a robust controller for stable operation. In response to this challenge, a novel second-order Active Disturbance-Rejection-Control (ADRC) is modeled as a secondary controller for performance studies. An extended state observer is designed for the estimation of system disturbance and uncertainties assisting ADRC in compensating for the impact through disturbance rejection. The magnetotactic bacteria-optimization approach is utilized to optimize the controller gains by reducing the errors in the objective function. Detailed case studies are carried out on two-area and three-area hybrid power-system incorporating different renewable energy plants to test the performance of the proposed controller. The dominance of the developed second-order-ADRC is verified based on system performance improvement concerning testified controllers available in the literature. The developed second-order-ADRC validates the robustness under different system-changed conditions. The fact that electric vehicles assist in system dynamic regulation is studied thoroughly. [ABSTRACT FROM AUTHOR]

A new dynamical system with self-adaptive dynamical stepsize is introduced for solving pseudomonotone mixed variational inequalities (MVIs). The globally stable convergence results of the proximal dynamical systems for solving pseudomonotone MVIs are established under some mild conditions. The upper bound formula of the convergence time of the proposed proximal dynamical systems is independent of the initial conditions. The proposed proximal dynamical system is also applied to solve composite optimization problems and minimax optimization problems. Finally, numerical examples are presented to validate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This article is devoted to the first steps of nine mathematicians from five countries on their path to mathematics, chaos and discrete dynamical systems, some from early childhood. In these life stories, the names of outstanding mathematicians arise, crisscrossing the nine stories in unexpected ways. These mathematicians also interacted with each other, forming an intriguing social network worldwide, across all borders of nationality and languages. [ABSTRACT FROM AUTHOR]

This paper deals with the leader-following consensus problem of Lur'e multi-agent systems (MASs) under undirected topologies, in which the leader has an unknown input. First, based only on the relative outputs among neighbouring agents, a distributed unknown input observer (UIO) is introduced to estimate the relative state of each follower, and the observation errors can exponentially converge to zero. Then, we propose an observer-based discontinuous controller with adaptive gains and demonstrate that the tracking errors can converge to zero. Subsequently, we further propose an observer-based continuous controller with adaptive gains under which chattering phenomenon can be avoided. Unlike the related works, both controllers can achieve leader-following consensus in a fully distributed manner, meaning that they do not depend on the global communication topology structure and the upper bound of the leader's input. Furthermore, two tractable algorithms are devised for computing the gain matrices. Finally, some simulation examples are presented on Chua's circuit system to validate the theoretical results. [ABSTRACT FROM AUTHOR]

Using the sawtooth map as the basis of a coupled map lattice enables simple analytic results to be obtained for the global Lyapunov spectra of a number of standard lattice networks. The results presented can be used to enrich a course on chaos or dynamical systems by providing tractable examples of higher dimensional maps and links to a number of standard results in matrices. A number of suggestions for classroom use are given. [ABSTRACT FROM AUTHOR]

Traumatic stress, suicide, and impulsive violence arguably are three of the most consequential problems facing societies today. Self-regulation shift theory is introduced to capture the underlying coping dynamics involved in these three grave challenges. Self-regulation shift theory, based in a nonlinear dynamical systems framework, focuses on critical psychological self-regulation thresholds and the role of cognitive self-appraisals in human adaptation to help understand these three significant societal challenges. This essay reviews existing evidence within the posttraumatic adaptation process utilizing SRST for understanding dynamic self-regulation. This is followed by integrating SRST within existing current theoretical models for suicidal behaviors and violent outbursts. The essay concludes with methodological suggestions for future research applying SRST and how this research offers important opportunities to develop early warning systems that promote hope when hope seems impossible. [ABSTRACT FROM AUTHOR]

The article presents the results of experimental and numerical simulation of oscillations of the structural nonlinear dynamic system under moving load. Laboratory tests were carried out on an experimental facility designed and manufactured by the authors to research the features of the dynamic behaviour of elastic-supported beam systems with displacement limiters. The obtained experimental data converge well with the obtained results by the calculations performed in the MATLAB environment based on the numerical algorithm developed by the authors using piecewise linear basis functions. The article evaluated the possibility of using the modern computational complex LS-Dyna for the analysis of oscillations of load-bearing systems with limiting supports. The influence of the speed of moving load, stiffness of beam, and elastic support on the features of the oscillations of the dynamic system is investigated. [ABSTRACT FROM AUTHOR]

A dynamic testing system consisting of a totally independent mechanical laboratory has been designed and constructed at the EUCENTRE Foundation. The results of a first experimental trial with the aim of checking the reliability of the system apparatus when stressed by imposing a series of dynamic loading histories on a real-scale two-storey tridimensional frame are presented. Particular care was devoted to equipment and its functioning, reliability of the digital controller, actuator response, and matching between reference input and feedback signal. Furthermore, a brief description regarding the behavior of the tridimensional frame and the experimental results is added. [ABSTRACT FROM AUTHOR]

This paper reviews information about a unique and iconic breed of the Orenburg Oblast, the homeland and the only place where the best herds of Orenburg down-hair goats in Russia are concentrated. Three types of these small ruminant animals are widespread on the territory of the region: Orenburg purebred gray goats, Orenburg purebred white goats, as well as crossbred white goats of F1 White Don × White Orenburg. Currently, at the farms of the Orenburg region, animals are selected according to their phenotype, with selected traits being color, weight and length of down hair. In recent years, the Orenburg goat breed has become an object of genetic research using various marker systems including immunogenetic, microsatellite, mtDNA and SNP markers. Overall, these studies evidence about the uniqueness of the allele pool in the landmark native breed of the Orenburg goats, which is a complex dynamic genetic system, prioritizing its further in-depth genome research and breeding applications. [ABSTRACT FROM AUTHOR]

The primary goal of this paper is to design a Multi-Converter Unified Power Quality Conditioner (MC-UPQC). The proposed method is solved based on the Synchronous Reference Frame (SRF) theory. The MC-UPQC involves two series Voltage Source Converters (VSCs) for power transfer between feeders to eliminate voltage sag, swell, interruption, and transient response in the system. The proposed model adopts control strategies based on an optimized Fuzzy Logic Controller (FLC) in SRF, utilizing a hybrid metaheuristic algorithm called Beetle Swarm-based Butterfly Optimization Algorithm (BS-BOA), which combines Beetle Swarm Optimization (BSO) and Butterfly Optimization Algorithm (BOA) for membership limit optimization and control rule generation. The major benefit of the optimized FLC-based MC-UPQC is its quick behavior in minimizing Total Harmonic Distortion (THD) in source and load side voltages and currents. Simulation and MATLAB environment are used for the entire system implementation. The comparative analysis of the proposed controller for MC-UPQC is performed against conventional controllers to validate its effectiveness. Quantitative data related to the main research outcomes, such as THD of source voltage and current, and dynamic behavior of the system, are included. The main benefit of the study is the significant reduction in THD and improved dynamic performance of the system. [ABSTRACT FROM AUTHOR]

With the increasing concerns over climate change and carbon emissions, fault detection and diagnostics (FDD) of low-global warming potential (GWP) refrigerant supermarket refrigeration systems has gained great attention from academic and industrial sectors. Various FDD approaches have been developed to detect, identify, and diagnose faults to save energy, improve food quality, and protect the environment. To mitigate the difficulty of collecting high-quality steady-state operational data in field operations faced by most model-based FDD methods, this study developed dynamic models of a low-GWP refrigerant (CO2) supermarket refrigeration system. The model accuracy was validated using manufacturer data and experimental data. Simulations were conducted to predict the system dynamic response under two common operational faults-evaporator air path blockage fault and the display case door open fault-to identify fault patterns and define key dynamic behavior indexes for supporting FDD algorithm development. [ABSTRACT FROM AUTHOR]

We present a new structure-preserving model order reduction (MOR) framework for large-scale port-Hamiltonian descriptor systems (pH-DAEs). Our method exploits the structural properties of the Rosenbrock system matrix for this system class and utilizes condensed forms which often arise in applications and reveal the solution behaviour of a system. Provided that the original system has such a form, our method produces reduced-order models (ROMs) of minimal dimension, which tangentially interpolate the original model's transfer function and are guaranteed to be again in pH-DAE form. This allows the ROM to be safely coupled with other dynamical systems when modelling large system networks, which is useful, for instance, in electric circuit simulation. [ABSTRACT FROM AUTHOR]

The boundary synchronisation problem of fractional-order fuzzy reaction–diffusion BAM neural networks with leakage delay is investigated. A novel adaptive boundary controller, Neumann boundary condition, and fuzzy feedback MIN and MAX templates of nonlinear dynamic fuzzy modelling are employed. We developed adaptive sufficient criteria to check the asymptotic stability of error dynamical system by using suitable Lyapunov functional, Wirtinger's inequality and LMI method, which guarantee the drive-response dynamical systems achieve the synchronisation. Meanwhile, two different controllers, adaptive full-domain and boundary controllers are developed. At last, numerical simulations are presented to demonstrate the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

We investigated the effects of international financial inflows (remittances, foreign direct investment and foreign aid) on economic complexity in Africa and the moderation role of institutional quality. We used the dynamic system GMM framework for a panel of 31 African countries over the period 2010–2020. We find that these international financial inflows are significant drivers of economic complexity in Africa, and that institutional quality is significantly moderating and enhancing their effects on economic complexity. Among other recommendations, we encourage policymakers in Africa to continually create an enabling environment to attract these financial inflows in order to promote sustainable investment and economic growth. [ABSTRACT FROM AUTHOR]

Steady states of dynamical systems, whether stable or unstable, are critical for understanding future evolution. Robust steady states, ones that persist under small changes in the model parameters, are desired when modelling ecological systems, where it is common for accurate and detailed information on functional form and parameters to be unavailable. Previous work by Jahedi et al. [Robustness of solutions of almost every system of equations, SIAM J. Appl. Math. 82(5) (2022), pp. 1791–1807; Structured systems of nonlinear equations, SIAM J. Appl. Math. 83(4) (2023), pp. 1696–1716.] has established criteria to imply the prevalence of robust steady states for systems with minimal predetermined structure, including conventional structured systems. We review that work and extend it by allowing symmetries in the system structure, which present added obstructions to robustness. [ABSTRACT FROM AUTHOR]

In this work, we first modify a Lotka–Volterra predator–prey system to incorporate an opportunistic predator and weak Allee effect in prey. The prey will be extinct if the combined effect of hunting and other food resources of predator is large. Otherwise, the dynamic behaviour of the system is extremely rich. A series of bifurcations such as saddle-node bifurcation, Hopf bifurcation, and Bogdanov–Takens bifurcation can happen. The validity of the theoretical results are supported with numerical simulations. [ABSTRACT FROM AUTHOR]