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• Correct an error in our paper published in Communications in Nonlinear Science and Numerical Simulation in 2015. • Construct a new Z 2 -equivariant cubic switching system and prove the existence of 15 limit cycles. • An approach is described for calculating the focus values of systems with two switching lines. In this note, we correct an error in our paper published in Communications in Nonlinear Science and Numerical Simulation in 2015 [5], in which the form of a Z 2 -equivariant cubic planar switching system is not correct. In this note, we add one more switching line and use the same equations given in [5] to construct a correct Z 2 -equivariant cubic system. Then, we prove that the new system can exhibit 15 limit cycles and therefore the conclusion given in [5] still holds. [ABSTRACT FROM AUTHOR]

In this paper, a novel framework for multi-agent systems is established to explore the swarm phenomenon of individuals with opinions in nature. Unlike the conventional researches in which agents in the system rigidly follow the predefined protocol, this paper combine opinions evolution with dynamic behaviors into multi-agent systems. To study the effect of opinions on behaviors, a protocol incorporating with opinions is introduced. The opinion of an agent is influenced by opinions of its neighbors and itself, while the behavior of the agent is influenced by both opinions and behaviors of agents. The existence and distributions of opinion equilibrium points are analyzed, and a necessary and sufficient condition of behavior stability is proposed. Moreover, the implementation of opinions leads to collective behavior, and the steady state of the system is analyzed. Finally, numerical simulations illustrate the effectiveness of the theoretical results. • A novel framework for multi-agent systems with dynamical opinions is established in the paper, by which agents will exhibit collective behavior. • Design an opinion updating strategy, and analyze the existence and distributions of opinion equilibrium points. • The behavior stability of the system is analyzed, and the steady states of the system are influenced by both opinions and behaviors of agents. [ABSTRACT FROM AUTHOR]

In this paper, we develop a nonconservative kinetic framework to be applied to the study of immune system dysregulation. From the modeling viewpoint, the model regards a system composed of stochastically interacting agents, under the action of an eternal force field. According to the application perspectives of this paper, the external force field has a specific analytical shape. In this case, some analytical results are proved, i.e. existence, uniqueness, positivity, and boundedness of solution of the related Cauchy problem, at least locally in time. Then, the model is refined to be implemented for the study of treatment strategies in case of autoimmune response. Specifically, we distinguish the autonomous case from the nonautonomous one, representing the absence or delivery of drugs, respectively. The former allows us to gain some stability results. Whereas, the latter is qualitatively studied. Numerical simulations are provided for both schemes. • A nonconservative kinetic model with external force field. • Solution existence, uniqueness, positivity, boundedness for nonautonomous system. • Kinetic system applied to autoimmune treatment strategy. [ABSTRACT FROM AUTHOR]

Anti-disturbance state estimation for reaction–diffusion neural networks (RDNNs) subject to persistent dwell-time (PDT) switching constraints is investigated in this paper. First, PDT switching that can be utilized to characterize both the fast and slow switching processes is used in this paper to accurately model the RDNNs. Moreover, by designing the time-sampling and space-splitting measurement algorithms, the proposed state estimator can significantly reduce the measurement cost while tolerating the frequent asynchrony of the system modes and estimator ones caused by the sensor update lag. Furthermore, a state estimator is constructed to obtain the state of RDNNs affected by matched disturbances. To suppress the impact of the disturbance on the system's state estimation, a disturbance observer and a disturbance-related controller are designed to estimate the disturbance information and ensure state estimation performance. Then, sufficient conditions for the proposed state estimator making the estimation error bounded are derived. Finally, numerical simulations for switched RDNNs with two-dimensional spatial diffusion are presented to illustrate the effectiveness and superiority of the proposed method. • Different from existing 1D spatial switched RDNNs, this paper focuses on switched RDNNs with high-dimensional diffusion and PDT switching rule, which are more in line with the system characteristics. • A combined time-sampling and space-splitting measurement method is proposed to reduce the measurement cost. To address the frequent asynchrony of system modes and estimator ones, stability analysis and estimator design are performed using iterative and recursive methods. • To obtain the system's state and to minimize the effect of disturbances on state estimation, an anti-disturbance state estimation scheme is proposed for PDT-switched RDNNs based on the disturbance observer. [ABSTRACT FROM AUTHOR]

This paper focuses on the p th moment exponentially stability for Markov switching and multi-impulse jumps stochastic time-varying delay system, where the switching behavior among subsystems of the target system is determined by Markov chains, and the occurrence of impulsive jumps is decided according to event-triggered impulsive mechanism when certain well-designed conditions are satisfied. By applying the Itô formula, Gronwall inequality and Razumikhin theorem, some novel sufficient criteria are provided to assure the system stability and get rid of Zeno phenomenon. It is worth pointing out that the multi-impulse jumps are our research aim and the range of delays considered is relatively wide, i.e., the daily bounded delay τ (t) ∈ [ 0 , 1) and the unupper bound delay τ (t) ∈ [ 1 , ∞). Subsequently, two diverse event trigger mechanism about impulsive jumps are proposed for such two types of delays, namely the defined event-triggered impulsive mechanism with delay. Finally, the validity and feasibility of the developed theoretical results are verified by two numerical simulations. • Different from the bounded delay system in Wang et al. (2023), Peng et al. (2021),Li and Zhu (2023),Peng et al. (2010), Zhu (2014), Zhua and Cao (2012),Yang and Zhu (2014), Xu and Zhu (2022), we discuss the daily bounded delay τ (t) ∈ [ 0 , 1) and the unupper bound delay τ (t) ∈ [ 1 , ∞). Two categories of event trigger impulsive method named event-triggered impulsive mechanism with delay (ETIMD) are proposed for two types delay, respectively. And in event-triggered condition, it fully consider the impact of delays. Moreover, the upper bound of the delay τ (t) ∈ [ 0 , 1) is required to avoid Zeno phenomenon. While for τ (t) ∈ [ 1 , ∞) , only the lower bound is required to escape Zeno phenomenon, in which is independent of the delayed upper bound. • Compared with Wang et al. (2022), Li et al. (2020), Peng et al. (2021), Zhu (2014), Xu and Zhu (2022), the Markov switching and multi-impulse jumps stochastic time-varying delay system as a benchmark is considered in this paper, where the switching behavior between subsystems is driven by Markov chains, and the occurrence of impulsive jump is decided according to ETIMD strategy. It should be emphasized that the multi-impulse jumps are the research goal. Thus, the system in [27,28,36,43] could be regarded as a special case of the stochastic delay system when the Markov switching is not considered in this study. • By applying the Itô formula, Gronwall inequality and Razumikhin theorem, some novel sufficient criteria of Lyapunov-Razumikhin type for p-ES are provided for unstable subsystems with stable impulses. [ABSTRACT FROM AUTHOR]

• Fixed-time synchronization of a class of memristor-based neural networks were investigated. • Two control schemes are proposed to achieve fixed-time synchronization. • The impulsive effects are overcomed. • Finally, an example and its simulations are given to demonstrate the feasibility of the obtained results. This paper concerns the fixed-time synchronization of a class of memristor-based neural networks with impulsive effects. Since impulses may destroy the synchronization, it is indispensable to design suitable controllers to control its unpredictable effects. In the present paper, two control schemes are proposed to achieve fixed-time synchronization of the impulsive memristor-based neural networks. Finally, two examples and their numerical simulations are presented to show the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper proposes a simple model of anomalous diffusion, in which a particle moves with the velocity field induced by a single "dipole" (a doublet or a pair of source and sink), whose moment is modulated randomly at each time step. A motivation to introduce such a model is that it may serve as a toy model to investigate an anomalous diffusion of fluid particles in turbulence. We perform a numerical simulation of the fractal dimension of the trajectory using periodic boundary conditions in two and three dimensions. For a wide range of the dipole moment, we estimate the fractal dimension of the trajectory to be 1.5–1.9 (2D) and 1.6–2.7 (3D). • This paper proposes a simple model of anomalous diffusion, in which a particle moves with the velocity field induced by a single "dipole" (a doublet or a pair of source and sink), whose moment is modulated randomly at each time step. • A motivation to introduce such a model is that it may serve as a toy model to investigate an anomalous diffusion of fluid particles in turbulence. • We perform a numerical simulation of the fractal dimension of the trajectory using periodic boundary conditions in two and three dimensions. • For a wide range of the dipole moment, we estimate the fractal dimension of the trajectory to be 1.5–1.9 (2D) and 1.6–2.7 (3D). [ABSTRACT FROM AUTHOR]

In this paper, a stochastic multi-weighted complex network with regime-switching diffusions (SMCNRSD) is considered. Here, the jump and the diffusion processes are interdependent, which generalizes the most existing network model. In the study of stochastic multi-weighted complex networks, stability analysis is an important topic. But so far, some work on stability requires stochastic multi-weighted complex networks to satisfy the global linear growth condition, which cannot be applied to some high-order or nonlinear networks. Therefore, one of the research contents of this study is to obtain the global existence and uniqueness of SMCNRSD under local conditions. Besides, the SMCNRSD usually does not stabilize spontaneously for reasons such as stochastic disturbance, multiple weights and nonlinear coupling. To stabilize SMCNRSD, periodic intermittent control is introduced to obtain the stability criterion. In application, stochastic multi-weighted Chua's circuits with regime-switching diffusions are taken into account. The corresponding existence and uniqueness as well as stability criteria are given under local conditions. To further illustrate the validity of theoretical results, numerical simulations are given. • The well-posedness of SMCNRSD is first proposed under the local conditions. • Regime-switching diffusions are introduced such that network model is more general. • Graph-theoretic method is a novel strategy to obtain the well-posedness of SMCNRSD. [ABSTRACT FROM AUTHOR]

• Sufficient conditions are established for a singular Cucker–Smale model with a general target motion pattern driving force to admit an asymptotic flocking. • A critical value of the exponent in the communication weight is given to lead to global regularity of solutions. • The avoiding collision asymptotic flocking of Cucker–Smale model with a general target motion pattern driving force is obtained for the first time in the literature. • It is the first time to show that the particles finally come to a line-shape formation with collision avoiding by theoretical proof in this paper. This paper is concerned with a singular Cucker–Smale model with a general targeted pattern driving force, which ensures that the particles finally come to the desired spatial configuration. Under some suitable conditions, we prove that the exponent α ≥ 1 in the communication weight leads to global regularity of solutions so that the system has an asymptotic flocking without collision between any agent. As an example, a prescribed driving force is given to demonstrate that the particles finally come to a line-shaped formation with collision avoidance, which can be viewed as a reasonable explanation for the wild geese flying in a line-shape in the sky. Moreover, this mechanism can be applied to the UAVs forming a line-shape to complete some special military missions. These results are novel, which are illustrated by both theoretical analysis and numerical simulations. [ABSTRACT FROM AUTHOR]

Highlights • We firstly propose a new periodically intermittent discrete observation control. • Synchronization issue of unified fractional-order chaotic coupled systems is discussed. • The method combined graph theory with Lyapunov method is adopted successfully. • We take nonlinear coupling term into account in our model, which is more general. Abstract In this paper, we propose a novel control technique, named as periodically intermittent discrete observation control (PIDOC), to investigate the synchronization issue of fractional-order coupled systems. Distinguished from periodically intermittent control which is widely applied in control fields, PIDOC proposed in this paper adopts discrete-time state observations in work time during a control period. In this way, PIDOC is more reasonable and available than traditional periodically intermittent control based on continuous-time state observations. Moreover, different from previous work about synchronization of fractional-order coupled systems, coupling term considered in this paper is nonlinear, which is more general. Then, combining graph theory with Lyapunov method, several synchronization criteria are obtained. Next, we successfully employ PIDOC to investigate synchronization of unified fractional-order chaotic coupled systems. Finally, two numerical simulations are presented to verify the validity of our theoretical results and the effectiveness of control scheme. [ABSTRACT FROM AUTHOR]

With the increasing demand for the accuracy of numerical simulation of pavement mechanics, the variational inequality model and its induced finite element method which can simulate the interlayer contact state becomes a potential solution. In this paper, a layer decomposition algorithm for solving variational inequality models of multi-layer elastic contact systems with interlayer Tresca friction conditions is studied. Continuous and discrete versions of the algorithm and their convergence theorems have been proposed and proved successively. Then, the algebraic form of the executable optimization algorithm and the numerical experimental results verify the practicability of the variational inequality model and its algorithm in the pavement mechanics modeling. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new iterative technique with a variable anchoring operator for reckoning the solution of a variational inequality problem over the set of the common fixed points of a nearly nonexpansive sequence of operators in the framework of Hadamard manifolds. We also establish a convergence result on the proposed algorithm for approximating a solution of the problem, under suitable assumptions. We apply our results for finding the solutions of a system of nonlinear equations, and of inclusion problems to support their utility. Our work improves results in the recent literature. Numerical simulations are given for a better understanding of the effectiveness of our outcomes. [ABSTRACT FROM AUTHOR]

• Construct a new 4D chaotic system and discuss the generation of multi-wing from equilibrium. • Consider smooth function to generate multi-wing. • The multi-wing chaotic system becomes a hyper chaotic system and the complexity is improved more conducive to synchronization control. • The design of robust synchronization controllers using fast terminal sliding mode and predefined time synchronization theory completes the predefined time synchronization between a 3D system and a multi-wing hyperchaotic system. In this paper, the construction of multi-wing chaotic system and predefined time synchronization are investigated. First, a new 4D chaotic system is constructed, and the existence of chaotic attractors is proved by dissipativity, boundedness, and Lyapunov exponents. Then the existence of a saddle focus of index-2 is proved by equilibrium point analysis, and a multi-winged hyperchaotic system is generated by extending the saddle focus with the constructed smooth function, which is found to be more complex and more conducive to synchronization applications by complexity analysis. Then the simulation of the circuit also proves the chaotic properties of the system in a physical sense. Finally, a new robust controller is designed using the fast terminal sliding mode algorithm to achieve predefined time synchronization between heterogeneous chaotic systems, and the numerical simulation results indicate that this synchronization method has a rapid time of convergence and achieves the predefined time effect. [ABSTRACT FROM AUTHOR]

This paper aims to investigate a thermal frictional contact model with damage and long memory effects. We consider a deformable body made of viscoelastic material and assume the process to be dynamic. The material is expected to adhere to the Kelvin–Voigt constitutive law, with damage and thermal effects incorporated. The variational formulation of the model results in a coupled system comprising a history-dependent hemivariational inequality governing the displacement field, a parabolic variational inequality describing the damage field and an evolution equation for the temperature field. In the analysis of this system, we initially introduce a fully discrete scheme, and then concentrate on deriving error estimates of numerical solutions. An optimal order error estimate is attained under some appropriate solution regularity assumptions. At the tail of this manuscript, numerical simulations are provided for the contact problem to validate the theoretical results. • We have studied a complex thermoviscoelastic contact model with damage and long memory. • The variational formulation gives rise to a differential hemivariational inequality. • We focus on optimal error estimates of numerical solutions. • Theoretical analysis and numerical simulation have faced considerable challenges. [ABSTRACT FROM AUTHOR]

The issue of group consensus for heterogeneous fractional-order multi-agent systems under the cooperation-competition networks with time delays is investigated in this paper. Novel group consensus control protocols with input and communication delays are designed based on cooperative-competitive interaction. The considered multi-agent systems consists of fractional order dynamics with the single integrator and the double integrator, and the speed of agents is not known. The matrix theory, frequency domain approach and graph theory are used to figure out the sufficient conditions for group consensus under the switching and fixed topology, respectively. Finally, numerical simulation examples are given to verify the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the issue of fixed-time intralayer synchronization of stochastic switched duplex networks (SSDNs) with limited communication. Firstly, control scheme without sign function is created to explore intralayer synchronization of SSDNs within a fixed time, and the control gains can vary with the error information. By the Lyapunov functional method, some novel synchronization criteria are established. In addition, by means of introducing the channel matrices, this paper considers the limited communication. Moreover, numerical simulation indicates the correctness of our theoretical result. Finally, from the perspective of the application, image encryption is demonstrated to confirm our theoretical implementation. • The switched duplex networks with stochastic disturbances are considered. • Synchronization criteria are obtained via fixed-time and finite-time control. • Limited communication is considered by introducing channel matrices. • Image encryption is realized based on our theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with the modeling of the management of the energy-demand in a microgrid network connected to a macrogrid network by means of a generalized kinetic theory model. Specifically the microgrid network N , composed of three energy sources, is connected to an external energy distribution network N e. The role of the network N e is to manage the absorption of the energy in the network N. The numerical investigations are addressed to the ability of the proposed model to reach the energy-demand. Specifically, a constant energy-demand and a time-dependent energy-demand are analyzed. The numerical simulation shows that the model is able to reproduce two different behaviors: on the one hand the three energy sources are able to satisfy the related energy-demand; on the other hand the three energy sources are not able to supply the prescribed amount of energy and the action of the external network N e is required. The operating mode of the network N , namely isolated (stand-alone) or connected to the external network N e , is shown by performing a sensitivity analysis on the functional parameters. Discussions and research perspectives are postponed to the last section of the paper. • Management of the energy-demand. • Microgrid network connected to a macrogrid network. • Generalized kinetic theory model. • Constant energy-demand and a time-dependent energy-demand. • Sensitivity analysis on the functional parameters. [ABSTRACT FROM AUTHOR]

A novel messages spreading model is suggested in this paper. The model is a natural generalization of the SIS (susceptible-infective-susceptible) model, in which two relevant messages with same probability of acceptance may spread among nodes. One of the messages has a higher priority to be adopted than the other only in the sense that both messages act on the same node simultaneously. Node in the model is termed as supporter when it adopts either of messages. The transition probability allows that two kinds of supports may transform into each other with a certain rate, and it varies inversely with the associated levels which are discretely distributed in the symmetrical interval around original point. Results of numerical simulations show that individuals tend to believe the messages with a better consistency. If messages are conflicting with each other, the one with higher priority would be spread more and another would be ignored. Otherwise, the number of both supports remains at a uniformly higher level. Besides, in a network with lower connected degree, over a half of the individuals would keep neutral, and the message with lower priority becomes harder to diffuse than the prerogative one. This paper explores the propagation of multi-messages by considering their correlation degree, contributing to the understanding and predicting of the potential propagation trends. [ABSTRACT FROM AUTHOR]

This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material. [ABSTRACT FROM AUTHOR]

This paper formulates a single-species stochastic chemostat model with periodic coefficients due to seasonal fluctuation. When the noise is small, a modified break-even concentration is identified, whose value below or above the averaged concentration of the input nutrient can completely determine whether the microorganism will persist or not, where an accuracy decay rate is given for extinction. In case of persistence, existence of the random positive periodic solution is proved for the considered model. Further, the random periodic solution is shown to be globally attractive under some mild extra condition. The periodic dynamics obtained in this paper are supported by computer simulations. [ABSTRACT FROM AUTHOR]

In this paper, we construct and analyze a reaction–diffusion hybrid model incorporating impulsive control and periodic evolution domain in Wolbachia -infected and wild mosquito populations to investigate the joint impact of spatial diffusion, impulsive control and the evolution of a domain on the control of mosquitoes. The explicit formulas of the two ecological reproduction indexes R U and R I are introduced, which relate to the evolution rate of domain and the impulsive function. Then we establish the threshold-type dynamics for the impulsive problem in terms of R U and R I by the method of upper and lower solutions, which present the extinction of mosquitoes, and competition and the coexistence of Wolbachia -infected and wild mosquitoes under impulsive control and periodic evolution domain. Numerically, we perform simulations to certify the analytical results, determine the importance of parameters on the persistence and extinction of mosquito populations, and expound how impulsive control, the evolution domain and fitness effect caused by Wolbachia affect the mosquito population evolution. • A model including impulsive control, Wolbachia and evolving domain is developed. • The formulas of the two ecological reproduction indexes (R U and R I) are derived. • The threshold dynamics in terms of R U and R I are fully solved. • Numerical simulations expound the effect of key parameters on the mosquitoes. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new numerical simulation iterative algorithm to solve the split feasibility problem and the fixed point problem with demicontractive mappings. Our algorithm mainly involves primal-dual iterative, relaxed projection, inertial technique and self-adaptive step size. Under reasonable conditions, the strong convergence of our algorithm is established. Moreover, we provide some numerical simulation examples to demonstrate the efficiency of our iterative algorithm compared to existing algorithms in the other literature. [ABSTRACT FROM AUTHOR]

In this paper, the global exponential stability and stabilization problems are investigated for memristive neural networks (MNNs) with stochastic disturbances, spatial diffusions and distributed delays. The spatial diffusions are not assumed to be symmetric and distributed delays are relaxed to be unbounded. Then, the presented MNNs are modeled as a class of stochastic partial systems with hybrid delays. Based on nonsmooth analysis, the Lyapunov–Krasovskii functional and inequality approach, some simple algebraic criteria are derived for the global exponential stability as well as the stabilization via two kinds of designed feedback controllers. The derived criteria are easily verified and the obtained results are available for other delayed systems with or without stochastic disturbances and spatial diffusions. Finally, the stability and stabilization results are validated by numerical simulations. • The stochastic model with spatial diffusions and distributed delays is discussed. • The derived results are generalized and they contain previous ones as special cases. • The method is available for other stochastic delayed partial differential systems. • The space set of the spatial diffusions in our model is not symmetrical. • The distributed delays are unbounded. [ABSTRACT FROM AUTHOR]

In Electro-Osmotic Pumps (EOPs), a micro fluid flow is formed by applying an external electric field via two electrodes immersed in the electrolyte. The immersed electrodes, due to lying in the fluid flow path, can consider an obstacle that can negatively affect the flow inside the microchannel. This issue is usually neglected in studies performed on the electroosmotic flows. Concerning this motivation, in this paper, a novel concept of a multi-stage EOP (introduced earlier by the researchers) was investigated numerically where the electrodes were attached to the wall of the micropump so as not to obstruct the fluid flow and to facilitate the serialization of micropumps. A two-dimensional numerical code is developed to analyze the steady-state performance of the multi-stage EOP. The governing equations for the fluid flow, internal and external electric fields, and ion concentration distribution are solved using the Finite Volume method. The results showed that in the multi-stage EOP consisting of multiple micropumps connected in series, the maximum pressure of EOP will enhances by increasing the number of micropumps. In contrast, the maximum flow rate remains approximately constant. The relationship between the maximum pressure, and the strength of the applied external electric field, was also investigated based on the electric field strength, and the results were expressed as a mathematical correlation. [ABSTRACT FROM AUTHOR]

Continuous stirred tank reactor (CSTR) is a common reactor in the chemical industry. The accurate observation of the concentration conversion rate of the mixture and the internal temperature of the reaction vessel is a prerequisite for obtaining the desired mixture. This paper proposes a novel observer based on residual neural networks for CSTR systems. Firstly, the mathematical model of the CSTR reaction is given, as well as a detailed description of the structure and equations of the residual neural networks and the designed observer. Then the matrix method is used for the nonlinear isolation of the residual neural networks and the theory of quadratic constraints for nonlinear activation functions of the neural networks is applied. Thus, the convergence of the proposed observer is analyzed theoretically in detail. Finally, the numerical simulations are implemented to demonstrate that the proposed residual neural network-based observer can quickly and accurately observe the state changes during the CSTR reaction. • A novel residual neural network-based observer for CSTR is proposed. • The convergence analysis of the proposed observer is presented. • The selection of hyperparameters of the residual neural networks is given. • The effectiveness of the proposed observer is verified by numerical simulations. [ABSTRACT FROM AUTHOR]

With the requirements of users enhanced for wireless communication, the cooperative communication will become a development in tendency future. In this paper, a model based on complex networks with both preferential and random attachments is researched to solve an actual network-CCN (cooperative communication network). Firstly, the evolution of CCN is given by four steps with different probabilities. At the same time, the rate equations of nodes degree are presented to analyze the evolution of CCN. Secondly, the degree distribution is analyzed by calculating the rate equation and numerical simulation. Finally, the robustness of CCN is studied by numerical simulation with random attack and intentional attack to analyze the effects of degree distribution, average path length and average degree. The results of paper are more significant for building CCN to program the resource of communication. [ABSTRACT FROM AUTHOR]

This paper considers hybrid systems — dynamical systems that exhibit both continuous and discrete behavior. Usually, in these systems, interactions between the continuous and discrete dynamics occur when a pre-defined function becomes equal to zero, i.e., in the system occurs a zero-crossing (the situation where the function only "touches" zero is considered as the zero-crossing, as well). Determination of zero-crossings plays a crucial role in the correct simulation of the system in this case. However, for models of many real-life hybrid systems, such interactions may lead to the so-called Zeno executions, i.e., situations where the system undergoes an unbounded number of discrete transitions in a finite and bounded length of time. In this case, standard numerical methods of simulating the systems may fail, since the time between two transitions can decrease significantly leading to ill-conditioning of the simulation. Correct determination of zero-crossings for a complex real-life system can require a lot of computational resources and, as a consequence, slow down the simulation significantly. This paper presents a new way to execute the simulation generating time observations of the hybrid system dynamically using numerical infinitesimals introduced recently, allowing thus to determine zero-crossings more accurately. The proposed method allows to automatically detect zero-crossings with predefined accuracy and to analyze better the behavior of the system around the zero-crossings generating observations more densely, where it is necessary. Moreover, the search for zero-crossings is performed efficiently without re-evaluation of the whole system at each observation. To show the validity of the proposed algorithm, the well-known Bouncing Ball hybrid system has been studied and the obtained simulation results were compared with the standard method. • Hybrid systems exhibiting both continuous and discrete behavior are considered. • Standard simulation methods of hybrid systems can fail due to the Zeno effect. • A new method for simulating hybrid systems in presence of Zeno behavior is proposed. • Numerical infinitesimals are used for an accurate finding of zero-crossing points. • The Infinity Computer used in simulations increases the accuracy significantly. [ABSTRACT FROM AUTHOR]

Highlights: [•] A new theory of fractional-order heat transport is introduced in the paper. [•] Fractional operators involve non-local thermal exchanges in the conductor. [•] Non-local effects depend of generalized measures of relative temperatures. [•] Thermodynamic consistency has been assessed for diffusive/ballistic heat transfer. [•] Numerical simulations have been reported in the paper. [Copyright &y& Elsevier]

In this paper, we study a predator–prey model assuming that the prey population gathers together in herd and considering feeding satiation for the predator population as well. After analyzing the equilibrium points of the model, their stability and the existence of bifurcations we show the existence of multistability for three different equilibrium points via numerical simulations. This last analysis is performed using the bSTAB software and its extensions. It allows to compute the basin of stability values and to plot bifurcation diagram surfaces with respect to the model parameters. • A predator-prey model is studied assuming that the prey population gathers in herd. • The equilibrium points of the model are analyzed, as well as their stability. • We show the existence of multistability for three different equilibrium points. [ABSTRACT FROM AUTHOR]

In this paper, we construct two kinds of exponential SAV approach with relaxation (R-ESAV) for dissipative system. The constructed schemes are linear and unconditionally energy stable. They can guarantee the positive property of SAV without any assumption compared with R-SAV and R-GSAV approaches, preserve all the advantages of the ESAV approach and satisfy dissipation law with respect to a modified energy which is directly related to the original free energy. We also give the rigorous consistency estimates of the constructed schemes for the L 2 gradient flows. Moreover, the second version of R-ESAV approach is easy to construct high-order BDF k schemes. Especially for Navier–Stokes equations, we construct two kinds of novel schemes based on the R-ESAV method. Finally, ample numerical examples are presented to exhibit that the proposed approaches are accurate and effective. • R-ESAV schemes can improve the accuracy of the solution significantly compared with the original ESAV approach. • We construct two kinds of novel schemes based on the R-ESAV method for Navier–Stokes equations. • Only one linear system with constant coefficients at each time step needs to be solved. • The positive property of SAV without any assumption can be guaranteed. • Numerical simulations are tested to show that the modified energy equals to the original free energy at almost all times. [ABSTRACT FROM AUTHOR]

This paper aims to incorporate a high order diffusion term into a SIQR epidemic model with transient prophylaxis and lasting prophylaxis. The existence and uniqueness of the global positive solution is proven and we find a condition ensuring the extinction of an infectious disease. The existence of a stationary distribution for the stochastic epidemic model is investigated as well. Numerical simulations are conducted to support our theoretical results and an example of application with COVID-19 data from Canada is used to estimate the transmission rate and reproduction number associated with the stochastic model, while constructing a model fitting the data. • A stochastic SIQR epidemic model with higher-order perturbation is investigated. • The existence and uniqueness of the global positive solution are studied. • A stochastic threshold is established for extinction. • COVID-19 data from Canada are used to estimate the transmission rate. [ABSTRACT FROM AUTHOR]

This paper explores the integration and harmonization of an epidemic dynamics model and a resource production–inventory management model, aiming to identify optimal control strategies of epidemic containment. We begin with establishing a generalized optimal control model for epidemic dynamics, which offers a unified framework to verify the sufficient conditions for the existence of the optimal solutions to a class of epidemic optimal control models. Based on the model, a resource production–inventory dynamic model with learning ability is proposed to find optimal strategies of the medical resource management. Subsequently, we propose the optimal control model for a dynamics system of COVID-19 and explore the optimal strategies of the combined applications of vaccine and recommended treatment in comprehensive control of the epidemic. Finally, the viability of effective integration and coordination between the optimal control models of the epidemic dynamics and the resource production–inventory system is verified by numerical simulation and analytical analysis, and a new method is implemented for finding the optimal management strategy for epidemic control. Therefore, this study advances a more comprehensive understanding of the interplay between epidemic dynamics and resource management, illustrating the feasibility and efficacy of integrating multiple models to achieve optimal decisions in both theoretical and practical aspects of epidemic control. • Sufficient condition of optimal solution to a class of optimal control models is set. • New optimal control models of COVID-19 and production–inventory dynamics are set. • Vaccine and treatment based medical resource optimal management way is implemented. • A multi-model integrated approach of optimal epidemic control strategies is explored. [ABSTRACT FROM AUTHOR]

In this paper, we design two totally decoupled, linear and unconditionally energy stable schemes with first-order time accuracy for the multi-physics diffuse interface model of two-phase magnetohydrodynamic (MHD) problem. These schemes combine the semi-implicit stabilization method/invariant energy quadratization (IEQ) method for the phase-field equations, Gauge–Uzawa method for the MHD equations, with some subtle implicit–explicit treatments for nonlinear coupled terms. Then this strong nonlinear and coupled complex system is split into a series of small linear elliptic equations, which makes the calculation more efficient. Additionally, compared to the standard projection method, the given schemes can overcome the selection of the initial value about pressure p and the treatment of artificial boundary condition on p which can lead to boundary layers and lose accuracy. Finally, rigorous proof of unconditional energy stability and several simulations of numerical experiment are conducted to demonstrate the validity of the decoupled schemes. • Our schemes split nonlinear coupled MHD into elliptic type problems. • We establish the unconditional energy stabilities for the schemes. • Numerical simulations demonstrate the validity of the given schemes. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this letter is to confirm the achievements in and answer all the mentioned comments in . Meanwhile some other drawbacks in the comment paper are also presented in this paper. [Copyright &y& Elsevier]

Abstract: This paper deals with the synchronization problem for competitive neural networks with different time scales, as well as mixed time-varying delays (both discrete and distributed time-varying delays) and stochastic disturbance. By using stochastic analysis approaches and constructing a novel Lyapunov–Krasovskii functional, an adaptive feedback controller is proposed to guarantee the exponential synchronization of proposed competitive neural networks in terms of p-norm. The synchronization results presented in this paper generalize and improve many known results. This paper also presents an illustrative example and uses simulated results of this example to show the feasibility and effectiveness of the theoretical results. [Copyright &y& Elsevier]

Abstract: In this paper, an adaptive algorithm is proposed for synchronization of chaotic systems with different orders. A modular adaptive control strategy is applied to make states of the slave system track those of the master, despite the unknown parameters. One of the most advantages of the modularity approach, which is applied for the first time in chaos synchronization, is its flexibility in choosing identification and control modules and designing them completely independently. In this paper, a modified recursive least square algorithm is used to identify the unknown parameters of the slave system, and the control module is designed by means of two different algorithms. First it is designed based on active control method, and then, in order to synchronize with a lower energy, we design an optimal controller. The two methods are applied on a practical case study, and the results are compared. Two different dimensional neuron models, the HR neuron model and the cable model of cylindrical cell, are considered as the master and slave systems, respectively. Simulation results confirm the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper proposes a novel fractional-order sliding mode approach for stabilization and synchronization of a class of fractional-order chaotic systems. Based on the fractional calculus a stable integral type fractional-order sliding surface is introduced. Using the fractional Lyapunov stability theorem, a single sliding mode control law is proposed to ensure the existence of the sliding motion in finite time. The proposed control scheme is applied to stabilize/synchronize a class of fractional-order chaotic systems in the presence of model uncertainties and external disturbances. Some numerical simulations are performed to confirm the theoretical results of the paper. It is worth noticing that the proposed fractional-order sliding mode controller can be applied to control a broad range of fractional-order dynamical systems. [Copyright &y& Elsevier]

Abstract: This paper investigates the stabilization of three dimensional chaotic systems in a finite time by extending our previous method for chaos stabilization. Based on the finite-time stability theory, a control law is proposed to realize finite-time stabilization of three dimensional chaotic systems. In comparison with the previous methods, the controller obtained by our method is simpler than those. Moreover, the method obtained in this paper is suitable for a class of three dimensional chaotic systems. The efficiency of the control scheme is revealed by some illustrative simulations. [Copyright &y& Elsevier]

Highlights • Modeling and numerical simulations of a nonlinear system subjected to stochastic excitations. • Harmonic Balance Method (HBM) and shooting method for mechanical systems with stochastic excitations. • Comparisons between experiments and numerical simulations. Abstract This paper presents experiments and numerical simulations of a nonlinear clamped-clamped beam subjected to stochastic broadband excitations. Broadband excitations are performed experimentally in order to show the hardening effect and the enlargement of the response peak in the vicinity of the primary resonance, and to detect the presence of secondary peaks resulting from the harmonics generated by the primary resonance. Using the decomposition of a random signal into a multi-harmonic periodic equivalent signal, the shooting method and the Harmonic Balance Method (HBM) are used to simulate the response of the nonlinear clamped-clamped beam subjected to a stochastic excitation. The latter is modeled as a multi-harmonic periodic equivalent signal in order to be used by both the shooting method and the HBM. A periodogram strategy is used to ensure a good estimate of the resulting Power Spectral Density (PSD). The two nonlinear methods are compared in terms of computation time and precision. A specific attention is paid on correct use of these methods. Finally, comparison between experiments and numerical simulations are performed for different levels of stochastic excitations. Good correlations are observed thus validating the global nonlinear proposed strategy. [ABSTRACT FROM AUTHOR]

Highlights • We propose a novel discount strategy for WOM marketing (the IBD strategy). • We model the WOM spreading process as a dynamic model (the DPA model). • We investigate the dynamics of the DPA model. • We examine the effect of different factors on the expected net profit of the IBD strategy. • Based on the above study, we suggest some promotional strategies. Abstract This paper addresses the issue of discount pricing in word-of-mouth (WOM) marketing. First, we propose a novel discount strategy we refer to as the Influence-Based Discount (IBD) strategy, in which each buyer would enjoy a discount that is linearly proportional to his/her influence in the WOM network. For the purpose of evaluating the performance of an IBD strategy, we model the associated WOM spreading process as a higher-dimensional nonlinear differential dynamical system we refer to as the Dormant-Potential-Adopting (DPA) model. Next, we examine the dynamics of a DPA model through computer experiments. Thereby, we estimate the expected net profit of an IBD strategy and inspect how different factors influence this profit through numerical experiments. On this basis, we suggest some feasible promotional measures. [ABSTRACT FROM AUTHOR]

Highlights • Nonlocality is an essential feature in fractional calculus. • Methods neglecting nonlocality lead to wrong results. • Numerical evidence of poor results obtained by neglecting nonlocality is given. Abstract In the paper titled "New numerical approach for fractional differential equations" by Atangana and Owolabi (2018) [1], it is presented a method for the numerical solution of some fractional differential equations. The numerical approximation is obtained by using just local information and the scheme does not present a memory term; moreover, it is claimed that third-order convergence is surprisingly obtained by simply using linear polynomial approximations. In this note we show that methods of this kind are not reliable and lead to completely wrong results since the nonlocal nature of fractional differential operators cannot be neglected. We illustrate the main weaknesses in the derivation and analysis of the method in order to warn other researchers and scientist to overlook this and other methods devised on similar basis and avoid their use for the numerical simulation of fractional differential equations. [ABSTRACT FROM AUTHOR]

Highlights • We discuss the decay synchronization problem of CMTDNs. • We design a novel nonlinear feedback controller and a Lyapunov function. • Some sufficient conditions are derived to ensure the decay synchronization of CMTDNs/CMDNs. • The main results can easily extended to exponential synchronization, polynomial synchronization and logarithmic synchronization. • Two simulations are shown to present the correctness of the main results. Abstract In this paper, we discuss the decay synchronization of complex multi-links time-varying dynamic networks (CMTDNs) for the first time. The exponential synchronization, polynomial synchronization and logarithmic synchronization can be seen as the special cases of the decay synchronization. CMTDNs are more general and realistic than the complex network with the single-link. By virtue of the definitions of the ψ -type function and ψ -type stability, we give the definition of the decay synchronization of the drive-response CMTDNs. Some novel and easily validated sufficient conditions are deduced to ensure the decay synchronization of drive-response CMTDNs based on the Lyapunov stability theory with the help of a novel nonlinear feedback controller and a new Lyapunov–Krasovskii function. Finally, two numerical simulations have been given to verify the correctness of main results. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the adaptive synchronization problem for a class of stochastic delayed neural networks. Based on the LaSalle invariant principle of stochastic differential delay equations and the stochastic analysis theory as well as the adaptive feedback control technique, a linear matrix inequality approach is developed to derive some novel sufficient conditions achieving complete synchronization of unidirectionally coupled stochastic delayed neural networks. In particular, the synchronization criterion considered in this paper is the globally almost surely asymptotic stability of the error dynamical system, which has seldom been applied to investigate the synchronization problem. Moreover, the delays proposed in this paper are time-varying delays and distributed delays, which have rarely been used to study the synchronization problem for coupled stochastic delayed neural networks. Therefore, the results obtained in this paper are more general and useful than those given in the previous literature. Finally, two numerical examples and their simulations are provided to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Variable-pitch cutter and spindle speed variation are two well-known methods to suppress milling chatter by disrupting regenerative effect. Considering their compatibility in practical application, their combined system perhaps has better potential for chatter suppression. However, to authors’ knowledge, there has been little research associated with this issue. In this paper, a milling dynamic model, which can simultaneously take into account the effect of the variations of cutter pitch angles and spindle speed, is constructed and linear stability analyses are carried out via an updated semi-discretization method, which has great capability to predict the stability lobes of milling process with multiple time-periodic delays. Then, through comparisons with previously associated works along with time-domain simulations, the effectiveness of the proposed model is confirmed. Moreover, the combined influences of the new system and the main system parameters on stability are deeply evaluated and discussed by conducting lots of simulations. Results show that the combined milling process exhibits a great capability to avoid the onset of milling chatter and can result in nearly 3-fold increase in depth of cut than that of a tradition one, but 1-fold increase for the process with variable pitch cutter or variable spindle speed in some special cases. [ABSTRACT FROM AUTHOR]

Few literatures apply complex oligopoly dynamics theory in games of incomplete information. This paper aims at analyzing dynamic behaviors of Bayesian game. A dynamic Cournot model with asymmetric information is proposed based on adaptive expectation and bounded rationality. Theoretical analysis draws two important conclusions: firstly, Bayesian Nash equilibrium of dynamic Cournot duopoly model with two players of adaptive expectation is always globally asymptotically stable. Secondly, Bayesian Nash equilibrium of dynamic Cournot duopoly model with players of adaptive expectation and gradient rule based on marginal profit is locally asymptotically stable only when parameters satisfy certain conditions. In our model, a firm of uncertain cost function is designed. A probability parameter θ of private type which differentiates high cost and low cost is introduced. Bifurcation, or even chaos with respect to θ , is performed by simulation which implies that large possibility of high-cost production yields easier chaos in duopoly market. High adjustment speeds of output form a three-dimensional strange attractors region. The unstable system's negative impact on equilibrium output and profit highlights the importance of system stability. Chaos control is in order to stabilize the equilibrium of the improved dynamic Cournot model with asymmetric information. [ABSTRACT FROM AUTHOR]

This paper is concerned with a backward heat conduction problem with time-dependent thermal diffusivity factor in an infinite “strip”. This problem is drastically ill-posed which is caused by the amplified infinitely growth in the frequency components. A new regularization method based on the Meyer wavelet technique is developed to solve the considered problem. Using the Meyer wavelet technique, some new stable estimates are proposed in the Hölder and Logarithmic types which are optimal in the sense of given by Tautenhahn. The stability and convergence rate of the proposed regularization technique are proved. The good performance and the high-accuracy of this technique is demonstrated through various one and two dimensional examples. Numerical simulations and some comparative results are presented. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we provide numerical evidence, via graphics generated with the help of computer simulations, that switching the control parameter of a dynamical system belonging to a class of fractional-order systems in a deterministic way, one obtains an attractor which belongs to the class of all admissible attractors of the considered system. For this purpose, while a multistep numerical method for fractional-order differential equations approximates the solution to the mathematical model, the control parameter is switched periodically every few integration steps. The switch is made inside of a considered set of admissible parameter values. Moreover, the synthesized attractor matches the attractor obtained with the control parameter replaced with the averaged switched parameter values. The results are verified in this paper on a representative system, the fractional-order Lü system. In this way we were able to extend the applicability of the algorithm presented in earlier papers using a numerical method for fractional differential equations. [Copyright &y& Elsevier]

Abstract: This paper obtains the exact 1-soliton solution of the perturbed Korteweg–de Vries equation with power law nonlinearity. Both topological as well as non-topological soliton solutions are obtained. The solitary wave ansatz is used to carry out this integration. The domain restrictions are identified in the process and the parameter constraints are also obtained. Finally, the numerical simulations are implemented in the paper. [Copyright &y& Elsevier]

Abstract: This paper studies optical solitons with non-Kerr law nonlinearity, in the presence of inter-modal dispersion. The coefficients of group velocity dispersion, nonlinearity and inter-modal dispersion terms have time-dependent coefficients. The types of nonlinearity that are considered are Kerr, power, parabolic and dual-power laws. The solitary wave ansatz is used to carry out the integration of the governing nonlinear Schrödinger’s equation with time-dependent coefficients. Both, bright and dark optical solitons, are considered, in this paper. Finally, numerical simulations are also given in each of these cases. The only necessary condition for these solitons to exist is that these time-dependent coefficients of group velocity dispersion and inter-modal dispersion are Riemann integrable. [Copyright &y& Elsevier]

Abstract: The sign of unknown input coefficients is assumed to be known in most papers about the input uncertainties. In this paper, a Nussbaum gain method is adopted to cope with the situation that both the sign and the value of input are unknown. And the unknown parameters can be estimated under the situation of unknown sign of control. The synchronization is achieved for a class of hyperchaotic systems with unknown parameters and input uncertainties by adopting of the Nussbaum gain method and the global terminal adaptive method. And the conclusions are made as follows: First, the proposed method is effective in the situation that the sign of input is unknown. Second, the estimation of unknown parameters can be achieved only when the number of unknown parameters satisfied some condition and no uncertainty exist in the input of systems. Third, the unknown parameters cannot be estimated correctly with common adaptive method when there are input uncertainties in the system. But the Nussbaum gain method can get good result in the estimation of unknown parameters. At last, numerical simulations are done to show the effectiveness of the proposed method. [Copyright &y& Elsevier]