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Fibrous dysplasia (FD) is a mosaic non-inheritable genetic disorder of the skeleton in which normal bone is replaced by structurally unsound fibro-osseous tissue. There is no curative treatment for FD, partly because its pathophysiology is not yet fully known. We present a simple mathematical model of the disease incorporating its basic known biology, to gain insight on the dynamics of the involved bone-cell populations, and shed light on its pathophysiology. We develop an analytical study of the model and study its basic properties. The existence and stability of steady states are studied, an analysis of sensitivity on the model parameters is done, and different numerical simulations provide findings in agreement with the analytical results. We discuss the model dynamics match with known facts on the disease, and how some open questions could be addressed using the model., (© 2024. The Author(s), under exclusive licence to the Society for Mathematical Biology.)

Producing a high release speed is important in throwing sports such as baseball and the javelin throw. Athletes in throwing sports might be able to achieve a greater throwing speed by improving the effectiveness of the kinetic chain. In this study a two-dimensional computer simulation model of overarm throwing was used to examine the effect of changes in forearm mass and upper arm mass on the release speed of a lightweight (58 g) projectile. The simulations showed that increasing the mass of the forearm decreases release speed, whereas increasing the mass of the upper arm initially increases release speed. For a given forearm mass there is an optimal upper arm mass that produces the greatest release speed. However, the optimal upper arm mass (5-6 kg) is substantially greater than that of an average adult (2.1 kg). These results suggest that athletes might be able to throw faster if they had a stronger tapering of segment mass along the length of their arm. A stronger taper could be readily achieved by attaching weights to the upper arm or by using hypertrophy training to increase the mass of the upper arm. High-speed overarm throwing is a complex three-dimensional movement and this study was a preliminary investigation into the effect of arm segment mass on throwing performance. Further simulation studies using three-dimensional throwing models are needed to generate more accurate insights, and the predictions of the simulation studies should be compared to data from experimental intervention studies of throwing sports.

Waddington's epigenetic landscape is a classic metaphor for describing the cellular dynamics during the development modulated by gene regulation. Quantifying Waddington's epigenetic landscape by mathematical modeling would be useful for understanding the mechanisms of cell fate determination. A few computational methods have been proposed for quantitative modeling of landscape; however, to model and visualize the landscape of a high dimensional gene regulatory system with realistic details is still challenging. Here, we propose a Monte Carlo method for modeling the Waddington's epigenetic landscape of a gene regulatory network (GRN). The method estimates the probability distribution of cellular states by collecting a large number of time-course simulations with random initial conditions. By projecting all the trajectories into a 2-dimensional plane of dimensions i and j, we can approximately calculate the quasi-potential U(x i ,x j ,∗)=-ln P(x i ,x j ,∗), where P(x i ,x j ,∗) is the estimated probability of an equilibrium steady state or a non-equilibrium state. Compared to the state-of-the-art methods, our Monte Carlo method can quantify the global potential landscape (or emergence behavior) of GRN for a high dimensional system. The potential landscapes show that not only attractors represent stability, but the paths between attractors are also part of the stability or robustness of biological systems. We demonstrate the novelty and reliability of our method by plotting the potential landscapes of a few published models of GRN., (Copyright © 2020 Elsevier B.V. All rights reserved.)

We propose new symplectic networks (SympNets) for identifying Hamiltonian systems from data based on a composition of linear, activation and gradient modules. In particular, we define two classes of SympNets: the LA-SympNets composed of linear and activation modules, and the G-SympNets composed of gradient modules. Correspondingly, we prove two new universal approximation theorems that demonstrate that SympNets can approximate arbitrary symplectic maps based on appropriate activation functions. We then perform several experiments including the pendulum, double pendulum and three-body problems to investigate the expressivity and the generalization ability of SympNets. The simulation results show that even very small size SympNets can generalize well, and are able to handle both separable and non-separable Hamiltonian systems with data points resulting from short or long time steps. In all the test cases, SympNets outperform the baseline models, and are much faster in training and prediction. We also develop an extended version of SympNets to learn the dynamics from irregularly sampled data. This extended version of SympNets can be thought of as a universal model representing the solution to an arbitrary Hamiltonian system., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 Elsevier Ltd. All rights reserved.)

Societies differ in susceptibility to social influence and in the social network structure through which individuals influence each other. What implications might these cultural differences have for changes in cultural norms over time? Using parameters informed by empirical evidence, we computationally modeled these cross-cultural differences to predict two forms of cultural change: consolidation of opinion majorities into stronger majorities, and the spread of initially unpopular beliefs. Results obtained from more than 300,000 computer simulations showed that in populations characterized by greater susceptibility to social influence, there was more rapid consolidation of majority opinion and also more successful spread of initially unpopular beliefs. Initially unpopular beliefs also spread more readily in populations characterized by less densely connected social networks. These computational outputs highlight the value of computational modeling methods as a means to specify hypotheses about specific ways in which cross-cultural differences may have long-term consequences for cultural stability and cultural change.

Evidence suggests that both the interaction of so-called Merkel cells and the epidermal stress distribution play an important role in the formation of fingerprint patterns during pregnancy. To model the formation of fingerprint patterns in a biologically meaningful way these patterns have to become stationary. For the creation of synthetic fingerprints it is also very desirable that rescaling the model parameters leads to rescaled distances between the stationary fingerprint ridges. Based on these observations, as well as the model introduced by Kücken and Champod we propose a new model for the formation of fingerprint patterns during pregnancy. In this anisotropic interaction model the interaction forces not only depend on the distance vector between the cells and the model parameters, but additionally on an underlying tensor field, representing a stress field. This dependence on the tensor field leads to complex, anisotropic patterns. We study the resulting stationary patterns both analytically and numerically. In particular, we show that fingerprint patterns can be modeled as stationary solutions by choosing the underlying tensor field appropriately.

During neural development sensory stimulation induces long-term changes in the receptive field of the neurons that encode the stimuli. The Bienenstock-Cooper-Munro (BCM) model was introduced to model and analyze this process computationally, and it remains one of the major models of unsupervised plasticity to this day. Here we show that for some stimulus types, the convergence of the synaptic weights under the BCM rule slows down exponentially as the number of synapses per neuron increases. We present a mathematical analysis of the slowdown that shows also how the slowdown can be avoided.

RuleBuilder is a tool for drawing graphs that can be represented by the BioNetGen language (BNGL), which is used to formulate mathematical, rule-based models of biochemical systems. BNGL provides an intuitive plain text, or string, representation of such systems, which is based on a graphical formalism. Reactions are defined in terms of graph-rewriting rules that specify the necessary intrinsic properties of the reactants, a transformation, and a rate law. Rules also contain contextual constraints that restrict application of the rule. In some cases, the specification of contextual constraints can be verbose, making a rule difficult to read. RuleBuilder is designed to ease the task of reading and writing individual reaction rules or other BNGL patterns required for model formulation. The software assists in the reading of existing models by converting BNGL strings of interest into a graph-based representation composed of nodes and edges. RuleBuilder also enables the user to construct de novo a visual representation of BNGL strings using drawing tools available in its interface. As objects are added to the drawing canvas, the corresponding BNGL string is generated on the fly, and objects are similarly drawn on the fly as BNGL strings are entered into the application. RuleBuilder thus facilitates construction and interpretation of rule-based models.

This study examines the dynamic regulation process responding to an external stimulus. The damped oscillator model has been used to describe this process. However, the model does not allow a nonzero steady state, even though the oscillations may continue and do not necessarily damp toward zero. This study introduces the driven damped oscillator model which has an additional parameter to identify different patterns of the steady state. Three methods, generalized local linear approximation, continuous time structural equation modeling, and analytic solutions of differential equations are provided to estimate model parameters. A simulation study indicates that parameters in the driven damped oscillator model are well recovered. The model is then illustrated using a data set on the daily reports of sales after a sale promotion. Potential applications and possible expansions of this model are also discussed.

Ring oscillators are biochemical circuits consisting of a ring of interactions capable of sustained oscillations. The nonlinear interactions between genes hinder the analytical insight into their function, usually requiring computational exploration. Here, we show that, despite the apparent complexity, the stability of the unique steady state in an incoherent feedback ring depends only on the degradation rates and a single parameter summarizing the feedback of the circuit. Concretely, we show that the range of regulatory parameters that yield oscillatory behaviour is maximized when the degradation rates are equal. Strikingly, this result holds independently of the regulatory functions used or number of genes. We also derive properties of the oscillations as a function of the degradation rates and number of nodes forming the ring. Finally, we explore the role of mRNA dynamics by applying the generic results to the specific case with two naturally different degradation timescales., (© 2018 The Authors.)

The natural world presents us with a rich and ever-changing sensory landscape containing diverse stimuli that constantly compete for representation in the brain. When the brain selects a stimulus as the highest priority for attention, it differentially enhances the representation of the selected, "target" stimulus and suppresses the processing of other, distracting stimuli. A stimulus may be selected for attention while it is still present in the visual scene (predictive selection) or after it has vanished (post hoc selection). We present a biologically inspired computational model that accounts for the prioritized processing of information about targets that are selected for attention either predictively or post hoc. Central to the model is the neurobiological mechanism of "selective disinhibition" - the selective suppression of inhibition of the representation of the target stimulus. We demonstrate that this mechanism explains major neurophysiological hallmarks of selective attention, including multiplicative neural gain, increased inter-trial reliability (decreased variability), and reduced noise correlations. The same mechanism also reproduces key behavioral hallmarks associated with target-distracter interactions. Selective disinhibition exhibits several distinguishing and advantageous features over alternative mechanisms for implementing target selection, and is capable of explaining the effects of selective attention over a broad range of real-world conditions, involving both predictive and post hoc biasing of sensory competition and decisions., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

We examine two connectionist networks-a fractal learning neural network (FLNN) and a Simple Recurrent Network (SRN)-that are trained to process center-embedded symbol sequences. Previous work provides evidence that connectionist networks trained on infinite-state languages tend to form fractal encodings. Most such work focuses on simple counting recursion cases (e.g., anbn), which are not comparable to the complex recursive patterns seen in natural language syntax. Here, we consider exponential state growth cases (including mirror recursion), describe a new training scheme that seems to facilitate learning, and note that the connectionist learning of these cases has a continuous metamorphosis property that looks very different from what is achievable with symbolic encodings. We identify a property-ragged progressive generalization-which helps make this difference clearer. We suggest two conclusions. First, the fractal analysis of these more complex learning cases reveals the possibility of comparing connectionist networks and symbolic models of grammatical structure in a principled way-this helps remove the black box character of connectionist networks and indicates how the theory they support is different from symbolic approaches. Second, the findings indicate the value of future, linked mathematical and empirical work on these models-something that is more possible now than it was 10 years ago., (Copyright © 2013 Cognitive Science Society, Inc.)

In this article, anti‐unwinding sliding mode attitude maneuver control with predefined time is investigated for rigid spacecraft with input saturation. First, a nonsingular sliding function containing two equilibrium points is designed to ensure the predefined‐time convergence of system states and unwinding‐free performance of the closed‐loop system on the sliding phase. Then, an auxiliary system with a dynamic parameter is presented to compensate the impact of input saturation. With this parameter, the auxiliary system can handle input saturation that occurs. Based on the sliding function and the auxiliary system, an attitude maneuver controller is developed to guarantee the robustness of the closed‐loop system to bounded external disturbance. Under the designed controller, the states of the closed‐loop system are driven into a neighborhood of the sliding surface within a predefined time. Moreover, the unwinding phenomenon is also avoided on the reaching phase. Numerical simulation results illustrate the unwinding‐free performance and predefined‐time convergence of the closed‐loop system under the proposed control strategy. [ABSTRACT FROM AUTHOR]

In this article, we discuss sustainable harvesting using a Filippov predator–prey system, which can produce yield and at the same time prevent over-exploitation of bioresources. The model is composed of two subsystems and the dynamics switch from one to the other with the help of a switching condition. We have derived possible equilibria, their existence and stability conditions for the respective subsystems, along with a comprehensive analysis of their phase space. The local and global stability analysis of the two subsystems, with and without harvesting, are studied. Furthermore, for the Filippov system, we have performed bifurcation analysis for several key parameters like predation rate, threshold quantity and prey refuge. Some local and global sliding bifurcations are also observed for the system. The system is shown to have multiple stable steady states or multiple stable sliding cycles for some suitable choice of parameters. Numerical simulations are presented to illustrate the dynamical behaviour of the system. [ABSTRACT FROM AUTHOR]

This paper addresses the tracking control challenge in the diving motion system of a specific class of autonomous underwater vehicles (AUVs) characterized by a torpedo-like shape. A decoupled and reduced-order three degrees-of-freedom linearized diving motion model is employed for depth position control. A control law is synthesized using the immersion and invariance (I&I) technique to achieve the control objectives. The primary aim is to attain tracking by immersing a stable, lower-order target (second-order) dynamic system into a three-dimensional manifold, upon which the closed-loop system evolves. We address the regulation problem as a specialized instance of the tracking problem, with the reference input set as a predetermined known depth that requires regulation. The efficacy of the proposed control law is evaluated through simulation studies involving various scenarios. Robustness tests are conducted to assess the control law’s performance under modeling uncertainties and underwater disturbances. The computer simulation employs an AUV named MAYA, utilizing experimentally validated diving motion parameters. A comparative analysis is performed between the proposed control law and other benchmark controllers to gauge its performance. Additionally, the effectiveness of the proposed control law is confirmed by validating its application to the nonlinear model of the diving motion system. [ABSTRACT FROM AUTHOR]

In this work, we study the invasion dynamics of a stage-structured population located in a one-dimensional periodic lattice. With a biologically relevant hypothesis that the population diffuses in its immature stage, we derive a novel spatially heterogeneous population model with coupled local and nonlocal effects. Assuming a KPP-type structure, we obtain the existence and variational characterization of spreading speed by appealing to monotone dynamical system theories. Further, we study the dependence of the spreading speed on the dispersal rate of immature population; it turns out that there exists an optimal dispersal strategy to maximize the speed. Numerical simulations further suggest that such an optimal strategy is unique. [ABSTRACT FROM AUTHOR]

After coarse-graining a complex system, the dynamics of its macro-state may exhibit more pronounced causal effects than those of its micro-state. This phenomenon, known as causal emergence, is quantified by the indicator of effective information. However, two challenges confront this theory: the absence of well-developed frameworks in continuous stochastic dynamical systems and the reliance on coarse-graining methodologies. In this study, we introduce an exact theoretic framework for causal emergence within linear stochastic iteration systems featuring continuous state spaces and Gaussian noise. Building upon this foundation, we derive an analytical expression for effective information across general dynamics and identify optimal linear coarse-graining strategies that maximize the degree of causal emergence when the dimension averaged uncertainty eliminated by coarse-graining has an upper bound. Our investigation reveals that the maximal causal emergence and the optimal coarse-graining methods are primarily determined by the principal eigenvalues and eigenvectors of the dynamic system's parameter matrix, with the latter not being unique. To validate our propositions, we apply our analytical models to three simplified physical systems, comparing the outcomes with numerical simulations, and consistently achieve congruent results. [ABSTRACT FROM AUTHOR]

A five-dimensional hyperchaotic system is a dynamical system with five state variables that exhibits chaotic behavior in multiple directions. In this work, we incorporated a 5D hyperchaotic system with constant- and variable-order Caputo and the Caputo–Fabrizio fractional derivatives. These fractional 5D hyperchaotic systems are solved numerically. Through simulations, the chaotic behavior of these fractional-order hyperchaotic systems is analyzed and a comparison between constant- and variable-order fractional hyperchaotic systems is presented. [ABSTRACT FROM AUTHOR]

This paper considers output-based adaptive event-triggered control of saturated system with the dynamic anti-windup compensator. An adaptive event-triggered condition with a time-varying threshold function is proposed, under which the system has better performance in saving communication resources. A dynamic anti-windup compensator is employed to overcome the potential performance degradation caused by input saturation. For the prescribed dynamic anti-windup compensator, an optimization problem is proposed for enlarging the domain of attraction. Moreover, if dynamic anti-windup compensator is not given in advance, co-design of the dynamic anti-windup compensator and adaptive event-triggered condition is developed. In addition, the Zeno behavior is excluded by calculating the minimum triggering time interval. Finally, the theoretical result is verified by numerical simulation. [ABSTRACT FROM AUTHOR]

This paper presents a First-Order Recurrent Neural Network activated by a wavelet function, in particular a Morlet wavelet, with a fixed set of parameters and capable of identifying multiple chaotic systems. By maintaining a fixed structure for the neural network and using the same activation function, the network can successfully identify the three state variables of several different chaotic systems, including the Chua, PWL-Rössler, Anishchenko–Astakhov, Álvarez-Curiel, Aizawa, and Rucklidge models. The performance of this approach was validated by numerical simulations in which the accuracy of the state estimation was evaluated using the Mean Square Error (MSE) and the coefficient of determination ( r 2 ), which indicates how well the neural network identifies the behavior of the individual oscillators. In contrast to the methods found in the literature, where a neural network is optimized to identify a single system and its application to another model requires recalibration of the neural algorithm parameters, the proposed model uses a fixed set of parameters to efficiently identify seven chaotic systems. These results build on previously published work by the authors and advance the development of robust and generic neural network structures for the identification of multiple chaotic oscillators. [ABSTRACT FROM AUTHOR]

This paper proposes a two-dimensional modified Leslie–Gower predator–prey model with carry-over effects, fear, prey protection and additional food, including prey harvesting. For this, it assumes the carry-over effect with delay incorporated in the birth rate of the prey population and gestation delay in Leslie–Gower term of a predator, and supposes that the predator consumes the prey according to Holling type II functional response. This dynamical system is split into two groups, namely non-delayed and delayed systems, respectively. In the non-delayed system, first, we discuss positivity, boundedness solutions, and the existence of equilibria, especially finding the coexistence of interior equilibrium points under certain conditions. After that, local and global stabilities are systematically analyzed. In addition, we obtain the conditions of Hopf-bifurcation in terms of the growth rate of prey species, prey protection and preference rate of predator for the non-delayed system. Whereas in the delayed system, both the delays have an essential role in governing the dynamical system discussed in three cases, and each case found the Hopf-bifurcation parameters for which the system changes stability behavior into instability. At last, the numerical simulations have been carried out to verify the theoretical findings. [ABSTRACT FROM AUTHOR]

We present our ongoing work aimed at accelerating a particle‐resolved direct numerical simulation model designed to study aerosol–cloud–turbulence interactions. The dynamical model consists of two main components—a set of fluid dynamics equations for air velocity, temperature, and humidity, coupled with a set of equations for particle (i.e., cloud droplet) tracing. Rather than attempting to replace the original numerical solution method in its entirety with a machine learning (ML) method, we consider developing a hybrid approach. We exploit the potential of neural operator learning to yield fast and accurate surrogate models and, in this study, develop such surrogates for the velocity and vorticity fields. We discuss results from numerical experiments designed to assess the performance of ML architectures under consideration as well as their suitability for capturing the behavior of relevant dynamical systems. [ABSTRACT FROM AUTHOR]

Synchronous generator system is a complicated dynamic system for energy transmission, which plays an important role in modern industrial production. In this article, we propose some predictor-corrector methods and structure-preserving methods for a generator system based on the first benchmark model of subsynchronous resonance, among which the structure-preserving methods preserve a Dirac structure associated with the so-called port-Hamiltonian descriptor systems. To illustrate this, the simplified generator system in the form of index-1 differential-algebraic equations has been derived. Our analyses provide the global error estimates for a special class of structure-preserving methods called Gauss methods, which guarantee their superior performance over the PSCAD/EMTDC and the predictor-corrector methods in terms of computational stability. Numerical simulations are implemented to verify the effectiveness and advantages of our methods. [ABSTRACT FROM AUTHOR]

Symplectic numerical schemes for reversible dynamical systems predict the solution reliably over large times as well, and are a good starting point for extension to schemes for simulating irreversible situations like viscoelastic wave propagation and heat conduction coupled via thermal expansion occuring in rocks, plastics, biological samples etc. Dissipation error (artificial nonpreservation of energies and amplitudes) of the numerical solution should be as small as possible since it should not be confused with the real dissipation occurring in the irreversible system. In addition, the other well-known numerical artefact, dispersion error (artificial oscillations emerging at sharp changes), should also be minimal to avoid confusion with the true wavy behavior. The continuum thermodynamical aspects (respect for balances with fluxes, systematic constitutive relationships between intensive quantities and fluxes, the second law of thermodynamics with positive definite entropy production, and the spacetime-based kinematic viewpoint) prove valuable for obtaining such extended schemes and for monitoring the solutions. Generalizing earlier works in this direction, here, we establish and investigate such a numerical scheme for one-dimensional viscoelastic wave propagation in the presence of heat conduction coupled via thermal expansion, demonstrating long-term reliability and the applicability of thermodynamics-based quantities in supervising the quality of the solution. [ABSTRACT FROM AUTHOR]

Delayed dynamical system plays a vital role in describing the dynamical phenomenon of neural networks. In this article, we proposed a class of new BAM neural networks involving time delay. The traits of solution and bifurcation behavior of the established BAMneural networks involving time delay were probed into. First, the existence and uniqueness is discussed using a fixed point theorem. Second, the boundedness of solution of the formulated BAM neural networks involving time delay was analyzed by applying an appropriate function and inequality techniques. Third, the stability peculiarity and bifurcation behavior of the addressed delayed BAM neural networks were investigated. Fourth, Hopf bifurcation control theme of the formulated delayed BAM neural networks was explored by virtue of a hybrid controller. By adjusting the parameters of the controller, we could control the stability domain and Hopf bifurcation onset, which was in favor of balancing the states of different neurons in engineering. To verify the correctness of gained major outcomes, computer simulations were performed. The acquired outcomes of this article were new and own enormous theoretical meaning in designing and dominating neural networks. [ABSTRACT FROM AUTHOR]

This paper is devoted to the analytical study of traveling wave solutions to a generalized Boussinesq equation with nonlinear dispersion. Utilizing the bifurcation method of dynamical systems, the existence of compacton and peakon solutions are established. Under certain parameter conditions, the compacton and peakon solutions can be bifurcated by smooth periodic wave solutions, smooth solitary wave solutions, and singular cusp solutions. Numerical simulations are supplied to corroborate the analytical results. Some previous results are extended. [ABSTRACT FROM AUTHOR]

This study introduces a reduced-order leg dynamic model to simplify the controller design and enhance robustness. The proposed multi-loop control scheme tackles tracking control issues in legged robots, including joint angle and contact-force regulation, disturbance suppression, measurement delay, and motor saturation avoidance. Firstly, model predictive control (MPC) and sliding mode control (SMC) schemes are developed using a simplified model, and their stability is analyzed using the Lyapunov method. Numerical simulations under two disturbances validate the superior tracking performance of the SMC scheme. Secondly, an Nth-order linear active disturbance rejection control (LADRC) is designed based on a simplified model and optimization problems. The second-order LADRC-SMC scheme reduces the contact-force control error in the SMC scheme by ten times. Finally, a fourth-order LADRC-SMC with a Smith Predictor (LADRC-SMC-SP) scheme is formulated, employing each loop controller independently. This scheme simplifies the design and enhances performance. Compared to numerical simulations of the above and existing schemes, the LADRC-SMC-SP scheme eliminates delay oscillations, shortens convergence time, and demonstrates fast force-position tracking responses, minimal overshoot, and strong disturbance rejection. The peak contact-force error in the LADRC-SMC-SP scheme was ten times smaller than that in the LADRC-SMC scheme. The integral square error (ISE) values for the tracking errors of joint angles θ 1   and θ 2 , and contact force f , are 1.6636 × 1 0 − 28   r a d 2 ⋅ s , 1.7983 × 1 0 − 28   r a d 2 ⋅ s , and 1.8062 × 1 0 − 30   N 2 ⋅ s , respectively. These significant improvements in control performance address the challenges in single-leg dynamic systems, effectively handling disturbances, delays, and motor saturation. [ABSTRACT FROM AUTHOR]

In this paper, the qualitative behaviors of an important four-dimensional Lorenz system with wild pseudohyperbolic attractor that proposed in (Gonchenko et al 2021 Nonlinearity 34 2018–47) are considered. Here, we prove that the four-dimensional Lorenz system with varying parameters is global bounded according to Lyapunov's direct method. Furthermore, we provide a collection of global absorbing sets, where in addition we obtain the rate of the trajectories going from the exterior to the global absorbing set. In particular, we solve the critical case k → 0 + that cannot be resolved by using the previous methods. The fundamental qualitative behaviors are analyzed theoretically and numerically. We present bifurcation diagrams to further explore the complicated dynamical behaviors of this system. The period-doubling bifurcation phenomenon is found. To illustrate the efficiency of our method, we present numerical simulations to show the validity of our research results. Finally, we present some applications of our research results in this paper. [ABSTRACT FROM AUTHOR]

This paper considers predator–prey systems in which the predator adapts the search speed to prey's density. The prey admits the cost of fear because of the predator and moves between source–sink patches to escape from predation. Using dynamical systems theory, we demonstrate equilibrium stability, uniform persistence and bifurcations in the system. It is shown that enhancing the search speed of predator and/or decreasing prey's dispersal from the source to sink could promote persistence of the system, while increasing the fear cost would stabilize the system. Moreover, dispersal could make the prey persist in both source–sink patches, even drive the predator into extinction. The dispersal could also make the prey reach a total population abundance larger than that without dispersal, even larger than the carrying capacity. Asymmetry in dispersal plays a role in the persistence and abundance. A novel finding of this work is that dispersal may lead to results reversing those without dispersal. Numerical simulations illustrate and extend our results. This work is important in understanding complexity in predation systems. [ABSTRACT FROM AUTHOR]

Following Professor P-Y CHOU’s idea, i.e., to study numerical simulation of turbulence, it is necessary to analyse and solve the fluctuating velocity field, based on the first principles, the spatiotemporal low-dimensional optimal dynamical systems of multi-scale simulation method (LMS method) is established systematically in this work, and in its application to the numerical simulation of re-shock Richtmyer-Meshkov problem, the turbulent middle-scale flow field and an approximate solution of turbulence which is different from the DNS approximate solution of turbulence, are obtained for the first time; the numerical results show that LMS method can be used with fewer grids to obtain more accurate approximate solutions of turbulence. Several problems encountered in the research are solved first, which paved the road to construct LMS method. These problems are: based on the physical characteristics of turbulence, a new concept of large, middle and small scale decomposition of turbulence is proposed; calculation method of spatial correlation of box filtering is find; a long-standing logical error in the theory of turbulence modelling is pointed out and the concept of multi-scale turbulence models is suggested; essence and key of closure problem of turbulence are discussed and numerical method for overcoming the closure problem of turbulence is given. With the box filtering/the space grid average and in the sense of a large-scale grid, the essence of the LMS method is a new turbulence numerical simulation method that integrates the RANS, LES, DES and DNS. It is necessary to indicate that the LMS method can also serve as an auxiliary tool for turbulence model research to examine whether the turbulence model corresponding to each term in the SGS-scale/fluctuations equation is correct or not. [ABSTRACT FROM AUTHOR]

Our aim in this article is to study the well-posedness of the generalized logarithmic nonlinear Cahn-Hilliard equation with regularization and proliferation terms. We are interested in studying the asymptotic behavior, in terms of finite-dimensional attractors, of the dynamical system associated with the problem and majorate the rate of convergence between the solutions of the Cahn-Hilliard equation and the regularized one. Additionally, we present some further regularity results and subsequently prove a strict separation property of the solution. Finally, we provide some numerical simulations to compare the solution with and without the regularization term, and more. [ABSTRACT FROM AUTHOR]

The stochastic nonlinear Schrödinger model (SNLSM) in (1+1)-dimension with random potential is examined in this paper. The analysis of the evolution of nonlinear dispersive waves in a totally disordered medium depends heavily on the model under investigation. This study has three main objectives. Firstly, for the SNLSM, derive stochastic precise solutions by using the modified Sardar sub-equation technique. This technique is efficient and intuitive for solving such models, as shown by the generated solutions, which can be described as trigonometric, hyperbolic, bright, single and dark. Secondly, for obtaining numerical solutions to the SNLSM, the algorithms described here offer an accurate and efficient technique. Lastly, investigate the phase plane analysis of the perturbed and unperturbed dynamical system and the time series analysis of the governing model. The results show that the numerical and analytical techniques can be extended to solve other nonlinear partial differential equations in physics and engineering. The results of this study have a significant impact on how well we comprehend how solitons behave in physical systems. Additionally, they may serve as a foundation for the development of improved numerical techniques for handling challenging nonlinear partial differential equations. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of spreading properties and traveling wave solutions for a vector-host disease system, which models the invasion of vectors and hosts to a new habitat. Combining the uniform persistence idea from dynamical systems with the properties of the corresponding entire solutions, we investigate the propagation phenomena in two different cases: (1) fast susceptible vector; (2) slow susceptible vector when the disease spreads. It turns out that in the former case, the susceptible vector may spread faster than the infected vector and host under appropriate conditions, which leads to multi-front spreading with different speeds; while in the latter case, the infected vector and host always catch up with the susceptible vector, and they spread at the same speed. We further obtain the existence and nonexistence of traveling wave solutions connecting zero to the endemic equilibrium. We also conduct numerical simulations to illustrate our analytic results. [ABSTRACT FROM AUTHOR]

This article studies the problem of regional observability of an important class of time‐fractional evolution systems involving the Caputo time‐fractional derivative. The main goal here is to check the regional observability of the considered system in the desired subregion, ω$$ \omega $$, of the evolution domain, Ω$$ \Omega $$. We assume that the linear part of the studied system is approximately regionally observable in the desired subregion ω$$ \omega $$, and we add some reasonable hypotheses on the system's dynamic, A$$ A $$, as well as on the nonlinear operator N$$ N $$. Then, with the help of all these assumptions, we attempt to reconstruct the initial state of our system in the desired subregion ω$$ \omega $$. To do that, we propose an extension of the Hilbert uniqueness method (HUM) to semilinear fractional systems. The main advantage of the HUM approach is that it transforms the reconstruction problem into a solvability one, which is more practical. We also present an algorithm for reconstructing the initial state in ω$$ \omega $$, which leads to some successful numerical simulations. [ABSTRACT FROM AUTHOR]

In this study, we investigate the occurrence of dragon-king extreme events in a three-dimensional autonomous Shimizu–Morioka oscillator. We observe that the bounded chaotic oscillations transition into large amplitude extreme events at a critical value of the system control parameter triggered by an interior crisis. These extreme events exhibit a unique distribution characterized by the probability distribution function. We performed laboratory experiments and conducted rigorous numerical simulations on the Shimizu–Morioka oscillator to validate our findings. The results from both approaches are in excellent agreement and confirm extreme behavior in this autonomous system. Our study represents the first comprehensive investigation of extreme events in the Shimizu–Morioka oscillator, integrating experimental observations and numerical simulations. Also, we observed the dragon-king extreme events in both experimental and numerical studies. These findings enhance our understanding of extreme events and their potential applications in chaos-based dynamical systems, contributing to advancing this field. [ABSTRACT FROM AUTHOR]

The operator-splitting (OS) method for real-time substructure testing (RTST) provides explicit and unconditionally stable solutions for structures with softening type stiffness and damping has been widely used for precisely disclosing the seismic performance of structures with velocity-dependent specimens. However, the OS method for RTST provides only explicit target displacement and velocity but not an explicit target acceleration, so that it is essentially an implicit method for Dynamic real-time substructure testing (DRTST) with dynamic system specimens. For precisely disclosing the seismic performance of multiple-degree-of-freedom structures with dynamic system specimens, one improved OS method is proposed for DRTST in this paper. The methodology and stability of the proposed OS method are investigated, and the effectiveness of the proposed OS method is validated by numerical simulations and experimental tests. By using the predictor displacement, velocity, and acceleration approximations, the OS method is an explicit algorithm for DRTST. The stability analysis shows that the proposed OS method is conditionally stable for DRTST, and its stability limit decreases with the increase of the mass ratio and the stiffness ratio, while it increases first and then decreases with the increase of the damping ratio. The numerical and experimental results confirm the stability and accuracy of the OS method. The OS method for DRTST provides a practical and precise investigation strategy for structures with dynamic system specimens and may have broad application prospects in civil engineering. [ABSTRACT FROM AUTHOR]

This paper deals with the kinematic and dynamic analysis of a two-element robot model. We have solved the problem using inverse kinematics. The result is the plotted trajectory of the robot's end point along defined points of the robot's workspace. The angular quantities computed are the rotation angle, angular velocity and angular acceleration in each kinematic pair. Furthermore, an inverse dynamics problem is solved. The moments in the kinematic pairs are computed. Subsequently, using the direct dynamics problem, the correctness of the obtained solution is confirmed. The programs designed for the simulation of dynamical systems - Matlab/Simulink and SimMechanics - were used in the solution. The results are presented in the form of graphs and tables. [ABSTRACT FROM AUTHOR]

Due to the breadth and complexity of spatial motion, and the nonlinear coupling caused by multiple degree-of-freedom, the control difficulties of spatial cooperative multirobot system are two mainly aspects, the modeling method and the dispose of uncertainty. For modeling, the process of directly using ordinary methods such as Lagrange mechanics are very complex. For control, the external disturbances and imperceptible errors will lead to the instability of dynamic system, these factors are collectively referred to as uncertainty. In this paper, a universal modeling method based on spatial cooperative multirobot system was proposed, and an adaptive robust controller was designed to solve the control problems. Simplify the connection link into a load and divide the system into two symmetrical subsystems by disconnecting the load center. The inherent physical position and given trajectories were unified as constraints. The constraints applied on system are creatively converted into consistent standard form through the Udwadia-Kalaba (U-K) method, and the corresponding constraints can be generated easily from the Udwadia-Kalaba basic equations. In addition, a nominal term to stable the system and an adaptive term was added to the controller. The adaptive term works through an adaptive parameter, the parameter estimates the uncertainty bound, thus, only the boundedness of uncertainty should be known, and more accurate control input can be gained. Eventually, the correctness of the model and controller has been confirmed through numerical simulation. [ABSTRACT FROM AUTHOR]

This article extends previous disability models in a different and more detailed framework that contemplates both temporary and permanent disability. By introducing different degrees of disability, the paper contributes to the recent debate among empirical scholars on the growth of disability insurance programmes in several OECD countries. This approach allows us to analyse, and consequently compare, the consumption paths of able, temporarily disabled, and permanently disabled workers. Furthermore, in a numerical simulation, the analysis demonstrates that the system of dynamic incentives should adapt the disability benefits to the different disability statuses. [ABSTRACT FROM AUTHOR]

In this paper, a new mosquito population suppression model with stage and sex structure is constructed, which is composed of two sub-models switching each other. Sterile mosquitoes are released with period T and remain sexually active for time T ̄. For the case T ̄ < T , three thresholds T * , m * and c * are determined for the release period T and release amount c. According to the values of T and c in different ranges determined by these thresholds, we study the dynamical behavior of the system for different release strategies, mainly including the existence and stability of the mosquito-extinction equilibrium and positive periodic solutions. Finally, some numerical simulations are performed to illustrate our results. [ABSTRACT FROM AUTHOR]

We present a phase-amplitude reduction framework for analyzing collective oscillations in networked dynamical systems. The framework, which builds on the phase reduction method, takes into account not only the collective dynamics on the limit cycle but also deviations from it by introducing amplitude variables and using them with the phase variable. The framework allows us to study how networks react to applied inputs or coupling, including their synchronization and phase locking, while capturing the deviations of the network states from the unperturbed dynamics. Numerical simulations are used to demonstrate the effectiveness of the framework for networks composed of FitzHugh–Nagumo elements. The resulting phase-amplitude equations can be used in deriving optimal periodic waveforms or introducing feedback control for achieving fast phase locking while stabilizing the collective oscillations. [ABSTRACT FROM AUTHOR]

Droplet vibration is an important phenomenon in many technical applications. Correctly predicting the occurring behaviour such as droplet detachment is a challenge for numerical simulations. In this work, a so‐called Navier‐Stokes‐Korteweg model that couples a gas‐liquid phase field to the Navier‐Stokes equations is used to simulate a droplet on a horizontally vibrating surface. Additionally, the equilibrium state of a static droplet on a fixed wall is simulated and the eigenshapes of the static system are investigated. It is found that this static eigenvalue analysis yields possible modes of the dynamic system, and some of the obtained eigenshapes can be recovered in the dynamic simulation. [ABSTRACT FROM AUTHOR]

The occurrence of a disaster and the appearance of a new product are items of news that can reach many people rapidly. Decision-makers would like to know how many individuals will obtain such information. In this paper, we study the case in which there are spreaders who think that the news is true and others that claim it is false. We simulate the propagation of a rumour and propose an algorithm for estimating the parameters of the resulting dynamical system. The relation between the parameters defining the simulation and the dynamical system is also studied. We conclude that the simulation describes the phenomenon well, in particular when the method proposed in this paper is used to estimate the parameters. [ABSTRACT FROM AUTHOR]

In this work, we consider an adaptive control method, which is simpler and generalized to obtain some conditions on the parameters for hyperchaotic models determined by using a Lyapunov direct method. Further, an adaptive controller for synchronization is designed by using Lyapunov functions by which the deriving system and the response system can realize adaptive modified function projective synchronization up to scaling matrix. Numerical simulation of each system is discussed in detail with graphical results. The graphical results are presented in detail in order to validate the theoretical results. These results in this article generalize and improve the corresponding results of the recent works. [ABSTRACT FROM AUTHOR]

Dynamic thermal insulation systems (DTISs) can adapt to external environment conditions and help to reduce energy consumption and increase occupants' thermal comfort, contributing towards the mitigation of overheating. DTISs adjust their configuration to optimize heat transfer through the façade. In this study, the performance of a DTIS was assessed through laboratory tests and numerical simulation. The DTIS is based on the ventilation of an air gap that facilitates the heat exchanges between the exterior and the interior. To extend the results of the experimental campaign, a set of scenarios was assessed based on numerical simulation. The results of the laboratory tests showed that the R-value obtained when the mechanical ventilation of the air gap is off (insulation state) is 3.89 m2.°C/W. In comparison, when it is on (conductive state), the R-value is 1.56 m2.°C/W, which corresponds to a reduction of approximately 60%. The results of the simulations showed that, when the shading system was on, the higher U-value was useful more than 50% of the time with discomfort, increasing to 75% when the shading system was off. [ABSTRACT FROM AUTHOR]

This paper proposes and investigates a nonselective harvesting Lotka-Volterra predator-prey system that incorporates population closure and the fear effect of the prey. The boundary equilibrium and positive equilibrium are studied in terms of their local and global stability characteristics. Our research indicates that the proportion of commodities designated for harvesting has a significant impact on the dynamic behavior of the system. Meanwhile, dynamic behavior of the system is not affected by the fear effect of the prey species. To demonstrate the viability of the key findings, numerical simulations are performed. [ABSTRACT FROM AUTHOR]

Networks are widely used to model the interaction between individual dynamic systems. In many instances, the total number of units and interaction coupling are not fixed in time, and instead constantly evolve. In networks, this means that the number of nodes and edges both change over time. Various properties of coupled dynamic systems, such as their robustness against noise, essentially depend on the structure of the interaction network. Therefore, it is of considerable interest to predict how these properties are affected when the network grows as well as their relationship to the growth mechanism. Here, we focus on the time evolution of a network's Kirchhoff index. We derive closed-form expressions for its variation in various scenarios, including the addition of both edges and nodes. For the latter case, we investigate the evolution where single nodes with one or two edges connecting to existing nodes are added recursively to a network. In both cases, we derive the relations between the properties of the nodes to which the new node connects along with the global evolution of network robustness. In particular, we show how different scalings of the Kirchhoff index can be obtained as a function of the number of nodes. We illustrate and confirm this theory via numerical simulations of randomly growing networks. [ABSTRACT FROM AUTHOR]