The problem of stabilizing a class of large-scale non-linear multiple delay systems is considered.The complicated system is decomposed into several subsystems; each function of them is expressed by a set of components...The problem of stabilizing a class of large-scale non-linear multiple delay systems is considered.The complicated system is decomposed into several subsystems; each function of them is expressed by a set of components of the overall state vector,with interconnections between them, and the subsystems are coupled by the delayed state. In this paper, a method is devised to be a suitable choice of state feedback controls of every subsystems, moreover, it is proved that the large-scale system is exponential stable.展开更多
The stability analysis of Cohen-Grossberg neural networks with multiple delays is given. An approach combining the Lyapunov functional with the linear matrix inequality （LMI） is taken to obtain the sufficient condit...The stability analysis of Cohen-Grossberg neural networks with multiple delays is given. An approach combining the Lyapunov functional with the linear matrix inequality （LMI） is taken to obtain the sufficient conditions for the globally asymptotic stability of equilibrium point. By using the properties of matrix norm, a practical corollary is derived. All results are established without assuming the differentiability and monotonicity of activation functions. The simulation samples have proved the effectiveness of the conclusions.展开更多
Active control of a flexible cantilever plate with multiple time delays is investigated using the discrete optimal control method. A controller with multiple time delays is presented. In this controller, time delay ef...Active control of a flexible cantilever plate with multiple time delays is investigated using the discrete optimal control method. A controller with multiple time delays is presented. In this controller, time delay effect is incorporated in the mathematical model of the dynamic system throughout the control design and no approximations and assumptions are made in the controller derivation, so the system stability is easily guaranteed. Furthermore, this controller is available for both small time delays and large time delays. The feasibility and efficiency of the proposed controller are verified through numerical simulations in the end of this paper.展开更多
The idea of network splitting according to time delay and weight is introduced.Based on the cyber physical systems(CPS),a class of multi-weighted complex transportation networks with multiple delays is modeled.The fin...The idea of network splitting according to time delay and weight is introduced.Based on the cyber physical systems(CPS),a class of multi-weighted complex transportation networks with multiple delays is modeled.The finite-time synchronization of the proposed complex transportation networks model is studied systematically.On the basis of the theory of stability,the technique of adaptive control,aperiodically intermittent control and finite-time control,the aperiodically intermittent adaptive finite-time synchronization controller is designed.The controller designed in this paper is beneficial for understanding the synchronization in multi-weighted complex transportation networks with multiple delays.In addition,the conditions for the existence of finite time synchronization have been discussed in detail.And the specific value of the settling finite time for synchronization is obtained.Moreover,the outer coupling configuration matrices are not required to be irreducible or symmetric.Finally,simulation results of the finite-time synchronization problem are given to illustrate the correctness of the results obtained.展开更多
New delay-independent and delay-dependent stability criteria for linear systems with multiple time-varying delays are established by using the time-domain method. The results are derived based on a new-type stability ...New delay-independent and delay-dependent stability criteria for linear systems with multiple time-varying delays are established by using the time-domain method. The results are derived based on a new-type stability theorem for general retarded dynamical systems and new analysis techniques developed in the author's previous work. Unlike some results in the literature, all of the established results do not depend on the derivative of time-varying delays. Therefore, they are suitable for the case with very fast time-varying delays. In addition, some remarks are also given to explain the obtained results and to point out the limitations of the previous results in the literature. Keywords Stability - Delay-independent criteria - Delay-dependent criteria - Linear time-delay systems - Multiple time-varying delays This work was supported by NSFC Key-Project (No. 60334010) and Guangdong Province Natural Science Foundation of China (No. 31406).展开更多
This paper is concerned with the optimal linear quadratic Gaussian(LQG)control problem for discrete time-varying system with multiplicative noise and multiple state delays.The main contributions are twofolds.First,in ...This paper is concerned with the optimal linear quadratic Gaussian(LQG)control problem for discrete time-varying system with multiplicative noise and multiple state delays.The main contributions are twofolds.First,in virtue of Pontryagin’s maximum principle,we solve the forward and backward stochastic difference equations(FBSDEs)and show the relationship between the state and the costate.Second,based on the solution to the FBSDEs and the coupled difference Riccati equations,the necessary and sufficient condition for the optimal problem is obtained.Meanwhile,an explicit analytical expression is given for the optimal LQG controller.Numerical examples are shown to illustrate the effectiveness of the proposed algorithm.展开更多
An optimal control method for seismic-excited building structures with multiple time delays is investigated in this paper. The system state equation with multiple time delays is discretized and transformed into a stan...An optimal control method for seismic-excited building structures with multiple time delays is investigated in this paper. The system state equation with multiple time delays is discretized and transformed into a standard discrete form without any explicit time delay by a particular augmenting for state variables. A time-delay controller is then designed based on this standard equation using the discrete optimal control method. Effectiveness of the proposed controller is demonstrated by numerical simulations. Simulation results indicate that a very small time delay may result in the instability of the control system if it is not compensated in the control design. Time delay may be compensated effectively by the proposed controller, in the mean time, an effective control may be obtained. The proposed controller is valid for both small and large time delays.展开更多
This paper is mainly concerned with stability analysis of neutral differential equations with multiple delays. Some criteria on instability, stability, asymptotic stability and exponential stability are obtained. The ...This paper is mainly concerned with stability analysis of neutral differential equations with multiple delays. Some criteria on instability, stability, asymptotic stability and exponential stability are obtained. The criterion on asymptotic stability is necessary and sufficient. Two examples are provided to illustrate the applications of our results. Some previous results are extended.展开更多
Global exponential stability problems are investigated for cellular neural networks （CNN） with multiple time-varying delays. Several new criteria in linear matrix inequality form or in algebraic form are presented t...Global exponential stability problems are investigated for cellular neural networks （CNN） with multiple time-varying delays. Several new criteria in linear matrix inequality form or in algebraic form are presented to ascertain the uniqueness and global exponential stability of the equilibrium point for CNN with multiple time-varying delays and with constant time delays. The proposed method has the advantage of considering the difference of neuronal excitatory and inhibitory effects, which is also computationally efficient as it can be solved numerically using the recently developed interior-point algorithm or be checked using simple algebraic calculation. In addition, the proposed results generalize and improve upon some previous works. Two numerical examples are used to show the effectiveness of the obtained results.展开更多
By Fourier analysis techniques and Schauder fixed point theorem, we study the existence of periodic solutions for a class of even order differential equations with multiple delays. The result obtained is a generalizat...By Fourier analysis techniques and Schauder fixed point theorem, we study the existence of periodic solutions for a class of even order differential equations with multiple delays. The result obtained is a generalization of the results developed by W. Layton to the case of multiple delays.展开更多
The HIV problem is studied by version of delay mathematical models which consider the apoptosis of uninfected CD4<sup>+</sup> T cells which cultured with infected T cells in big volume. The opportunistic i...The HIV problem is studied by version of delay mathematical models which consider the apoptosis of uninfected CD4<sup>+</sup> T cells which cultured with infected T cells in big volume. The opportunistic infection and the apoptosis of uninfected CD4<sup>+</sup> T cells are caused directly or indirectly by a toxic substance produced from HIV genes. Ubiquitously, the nonlinear incidence rate brings forth the increasing number of infected CD4<sup>+</sup> T cells with introduction of small time delay, and in addition, there also exists a natural time delay factor during the process of virus replication. With state feedback control of time delay, the bifurcating periodical oscillating phenomena is induced via Hopf bifurcation. Mathematically, with the geometrical criterion applied in the stability analysis of delay model, the critical threshold of Hopf bifurcation in multiple delay differential equations which satisfy the transversal condition is derived. By applying reduction dimensional method combined with the center manifold theory, the stability of the bifurcating periodical solution is analyzed by the perturbation near Hopf point.展开更多
This paper offeres an exact study on the robust stability of a kind of combined integrating control system, and the robust stability belongs to the analysis of a kind of quasi-polynomial with two independent time dela...This paper offeres an exact study on the robust stability of a kind of combined integrating control system, and the robust stability belongs to the analysis of a kind of quasi-polynomial with two independent time delays. The parameters of stable space under time delay uncertainty are fixed after Rekasius transformation, and then a new cluster treatment of characteristic roots (CTCR) procedure is adopted to determine the stable space. By this strategy we find that the unstable space is not continuous and both Karitonov vertices theory and Edge theory are unable to be extended to quasi-polynomial under time delay uncertainty.展开更多
This article investigates the asymptotic and finite-time synchronization of fractional-order multiplex neural networks with multiple delays.Initially,a novel extended Halanay-type inequality for fractional-order diffe...This article investigates the asymptotic and finite-time synchronization of fractional-order multiplex neural networks with multiple delays.Initially,a novel extended Halanay-type inequality for fractional-order differential equations with multiple delays is developed.Based on this framework,conditions are derived to achieve asymptotic synchronization by designing adaptive control schemes.Subsequently,novel sufficient criteria for achieving finite-time synchronization are established by introducing a hybrid control protocol that incorporates the Lyapunov method,inequality techniques,and a reduction to absurdity approach.Furthermore,the settling time for synchronization is explicitly estimated.In addition,the proposed methods are extended to in-vestigate asymptotic and finite-time synchronization for fractional-order multiplex neural networks with delay-free.In particular,the results represent a significant extension of the corresponding cases for integer-order systems.Finally,numerical simulations are provided to verify the theoretical findings.These results offer valuable insights into the synchronization of fractional-order networks with multiple delays,paving the way for scalable and practical solutions in areas such as secure communication and cross-layer integration in neural networks.展开更多
This paper analyzes the stability of milling with variable pitch cutter and tool runout cases characterized by multiple delays,and proposes a new variable-step numerical integration method for efficient and accurate s...This paper analyzes the stability of milling with variable pitch cutter and tool runout cases characterized by multiple delays,and proposes a new variable-step numerical integration method for efficient and accurate stability prediction. The variable-step technique is emphasized here to expand the numerical integration method,especially for the low radial immersion cases with multiple delays. First,the calculation accuracy of the numerical integration method is discussed and the variable-step algorithm is developed for milling stability prediction for single-delay and multiple-delay cases,respectively. The milling stability with variable pitch cutter is analyzed and the result is compared with those predicted with the frequency domain method and the improved full-discretization method. The influence of the runout effect on the stability boundary is investigated by the presented method. The numerical simulation shows that the cutter runout effect increases the stability boundary,and the increasing stability limit is verified by the milling chatter experimental results in the previous research. The numerical and experiment results verify the validity of the proposed method.展开更多
In this paper,we investigate an inertial two-neural coupling system with multiple delays.We analyze the number of equilibrium points and demonstrate the corresponding pitchfork bifurcation.Results show that the system...In this paper,we investigate an inertial two-neural coupling system with multiple delays.We analyze the number of equilibrium points and demonstrate the corresponding pitchfork bifurcation.Results show that the system has a unique equilibrium as well as three equilibria for different values of coupling weights.The local asymptotic stability of the equilibrium point is studied using the corresponding characteristic equation.We find that multiple delays can induce the system to exhibit stable switching between the resting state and periodic motion.Stability regions with delay-dependence are exhibited in the parameter plane of the time delays employing the Hopf bifurcation curves.To obtain the global perspective of the system dynamics,stability and periodic activity involving multiple equilibria are investigated by analyzing the intersection points of the pitchfork and Hopf bifurcation curves,called the Bogdanov-Takens(BT)bifurcation.The homoclinic bifurcation and the fold bifurcation of limit cycle are obtained using the BT theoretical results of the third-order normal form.Finally,numerical simulations are provided to support the theoretical analyses.展开更多
This paper is concerned with the consensus problems for second-order multi-agent systems with multiple input delays.Different from all standard consensus algorithms with uniform delays,the authors aim to find the larg...This paper is concerned with the consensus problems for second-order multi-agent systems with multiple input delays.Different from all standard consensus algorithms with uniform delays,the authors aim to find the largest input-delay margin which can guarantee the consensus for the case when delays are nonuniform.Based on frequency domain analysis and matrix theory,an upper bound for maximum tolerable input-delay is given in terms of the relationship with scaling strengths and largest eigenvalue of the Lapalician matrix.Simulation results are provided to illustrate the obtained results.展开更多
A system of delay differential equations is studied which represent a model for four neurons with time delayed connections between the neurons and time delayed feedback from each neuron to itself. The linear stability...A system of delay differential equations is studied which represent a model for four neurons with time delayed connections between the neurons and time delayed feedback from each neuron to itself. The linear stability and bifurcation of the system are studied in a parameter space consisting of the sum of the time delays between the elements and the product of the strengths of the connections between the elements. Meanwhile, the bifurcation set are drawn in the parameter space.展开更多
A coupled neural system with multiple delays has been investigated. The number of equilibrium points is analyzed. It implies that the neural system exhibits a unique equilibrium and three ones for the different values...A coupled neural system with multiple delays has been investigated. The number of equilibrium points is analyzed. It implies that the neural system exhibits a unique equilibrium and three ones for the different values of coupling weight by employing the pitchfork bifurcation of the trivial equilibrium point. Further, the local asymptotical stability of the trivial equilibrium point is studied by analyzing the corresponding characteristic equation. Some stability criteria involving multiple delays and coupling weight are obtained. The results show that the neural system exhibits the delay-independent and delay-dependent stability. Increasing delay induces stability switching between resting state and periodic motion in some parameter regions of coupling weight. In addition, the criterion for the global stability of the trivial equilibrium is also derived by constructing a suitable Lyapunov functional. Finally, some numerical simulations are taken to support the theoretical results.展开更多
The object of this article is to study the consequences of occurrence both fault in input and multiple time-varying delays simultaneously while designing observer to estimate the states of agents and also unknown nonl...The object of this article is to study the consequences of occurrence both fault in input and multiple time-varying delays simultaneously while designing observer to estimate the states of agents and also unknown nonlinear fault of system.Two delay dependent criteria are established to show the states of observer reach to states of MAS and also states of observer reach to consensus.From two obtained criteria,it can be deduced,by constructing a distributed controller-based observer design,MAS reach to consensus exponentially.Finally,the advantages of the obtained results are shown by solving an illustrative example.展开更多
文摘The problem of stabilizing a class of large-scale non-linear multiple delay systems is considered.The complicated system is decomposed into several subsystems; each function of them is expressed by a set of components of the overall state vector,with interconnections between them, and the subsystems are coupled by the delayed state. In this paper, a method is devised to be a suitable choice of state feedback controls of every subsystems, moreover, it is proved that the large-scale system is exponential stable.
基金This work was supported by the National Natural Science Foundation of China(No. 60534010, 60572070), Liaoning Natural Science Foundation ofChina(No.20052027), and the Program for Changjiang Scholars and Innovative Research Team in University.
文摘The stability analysis of Cohen-Grossberg neural networks with multiple delays is given. An approach combining the Lyapunov functional with the linear matrix inequality （LMI） is taken to obtain the sufficient conditions for the globally asymptotic stability of equilibrium point. By using the properties of matrix norm, a practical corollary is derived. All results are established without assuming the differentiability and monotonicity of activation functions. The simulation samples have proved the effectiveness of the conclusions.
基金the National Natural Science Foundation of China (Nos. 10772112 and 10472065)the KeyProject of Ministry of Education of China (No. 107043)the Specialized Research Fund for the Doctoral Program ofHigher Education of China (No. 20070248032).
文摘Active control of a flexible cantilever plate with multiple time delays is investigated using the discrete optimal control method. A controller with multiple time delays is presented. In this controller, time delay effect is incorporated in the mathematical model of the dynamic system throughout the control design and no approximations and assumptions are made in the controller derivation, so the system stability is easily guaranteed. Furthermore, this controller is available for both small time delays and large time delays. The feasibility and efficiency of the proposed controller are verified through numerical simulations in the end of this paper.
基金Project supported by the National Natural Science Foundation of China(Grant No.61803275)Liaoning Provincial Department of Education Scientific Research Fund Project,China(Grant Nos.lnjc202018 and lnzd202007)+1 种基金Liaoning BaiQianWan Talents Program(Grant No.2017076)Liaoning Province Doctor Starting Foundation(Grant No.20170520283).
文摘The idea of network splitting according to time delay and weight is introduced.Based on the cyber physical systems(CPS),a class of multi-weighted complex transportation networks with multiple delays is modeled.The finite-time synchronization of the proposed complex transportation networks model is studied systematically.On the basis of the theory of stability,the technique of adaptive control,aperiodically intermittent control and finite-time control,the aperiodically intermittent adaptive finite-time synchronization controller is designed.The controller designed in this paper is beneficial for understanding the synchronization in multi-weighted complex transportation networks with multiple delays.In addition,the conditions for the existence of finite time synchronization have been discussed in detail.And the specific value of the settling finite time for synchronization is obtained.Moreover,the outer coupling configuration matrices are not required to be irreducible or symmetric.Finally,simulation results of the finite-time synchronization problem are given to illustrate the correctness of the results obtained.
文摘New delay-independent and delay-dependent stability criteria for linear systems with multiple time-varying delays are established by using the time-domain method. The results are derived based on a new-type stability theorem for general retarded dynamical systems and new analysis techniques developed in the author's previous work. Unlike some results in the literature, all of the established results do not depend on the derivative of time-varying delays. Therefore, they are suitable for the case with very fast time-varying delays. In addition, some remarks are also given to explain the obtained results and to point out the limitations of the previous results in the literature. Keywords Stability - Delay-independent criteria - Delay-dependent criteria - Linear time-delay systems - Multiple time-varying delays This work was supported by NSFC Key-Project (No. 60334010) and Guangdong Province Natural Science Foundation of China (No. 31406).
文摘This paper is concerned with the optimal linear quadratic Gaussian(LQG)control problem for discrete time-varying system with multiplicative noise and multiple state delays.The main contributions are twofolds.First,in virtue of Pontryagin’s maximum principle,we solve the forward and backward stochastic difference equations(FBSDEs)and show the relationship between the state and the costate.Second,based on the solution to the FBSDEs and the coupled difference Riccati equations,the necessary and sufficient condition for the optimal problem is obtained.Meanwhile,an explicit analytical expression is given for the optimal LQG controller.Numerical examples are shown to illustrate the effectiveness of the proposed algorithm.
基金supported by the National Natural Science Foundation of China (Nos.10772112,10472065)the Key Project of Ministry of Education of China (No.107043)+2 种基金the Key Scientific Project of Shang-hai Municipal Education Commission (No.09ZZ17)the Specialized Research Fund for the DoctoralProgram of Higher Education of China (No.20070248032)the Research Project of State Key Laboratory of Ocean Engineering of China (No.GKZD010807)
文摘An optimal control method for seismic-excited building structures with multiple time delays is investigated in this paper. The system state equation with multiple time delays is discretized and transformed into a standard discrete form without any explicit time delay by a particular augmenting for state variables. A time-delay controller is then designed based on this standard equation using the discrete optimal control method. Effectiveness of the proposed controller is demonstrated by numerical simulations. Simulation results indicate that a very small time delay may result in the instability of the control system if it is not compensated in the control design. Time delay may be compensated effectively by the proposed controller, in the mean time, an effective control may be obtained. The proposed controller is valid for both small and large time delays.
基金Supported by the National Natural Science Foundation of China (Grant Nos.1137102711071001+8 种基金11201248)Research Fund for Doctoral Program of Higher Education of China (Grant No.20123401120001)Program of Natural Science Research in Anhui Universities (Grant Nos.KJ2013A032KJ2011A020)Anhui Provincial Natural Science Foundation (Grant No.1208085MA13)Scientific Research Starting Fund for Doctor of Anhui University (Grant Nos.023033190001023033190181)the 211 Project of Anhui University (Grant Nos.KJQN100102303050055)
文摘This paper is mainly concerned with stability analysis of neutral differential equations with multiple delays. Some criteria on instability, stability, asymptotic stability and exponential stability are obtained. The criterion on asymptotic stability is necessary and sufficient. Two examples are provided to illustrate the applications of our results. Some previous results are extended.
基金the National Natural Science Foundation of China (No.60274017, 60325311).
文摘Global exponential stability problems are investigated for cellular neural networks （CNN） with multiple time-varying delays. Several new criteria in linear matrix inequality form or in algebraic form are presented to ascertain the uniqueness and global exponential stability of the equilibrium point for CNN with multiple time-varying delays and with constant time delays. The proposed method has the advantage of considering the difference of neuronal excitatory and inhibitory effects, which is also computationally efficient as it can be solved numerically using the recently developed interior-point algorithm or be checked using simple algebraic calculation. In addition, the proposed results generalize and improve upon some previous works. Two numerical examples are used to show the effectiveness of the obtained results.
基金The second author partially supported by NSFC (10571179, 10871203) GrantProgramfor New Century Excellent Talents in University of Ministry of Eduction of China
文摘By Fourier analysis techniques and Schauder fixed point theorem, we study the existence of periodic solutions for a class of even order differential equations with multiple delays. The result obtained is a generalization of the results developed by W. Layton to the case of multiple delays.
文摘The HIV problem is studied by version of delay mathematical models which consider the apoptosis of uninfected CD4<sup>+</sup> T cells which cultured with infected T cells in big volume. The opportunistic infection and the apoptosis of uninfected CD4<sup>+</sup> T cells are caused directly or indirectly by a toxic substance produced from HIV genes. Ubiquitously, the nonlinear incidence rate brings forth the increasing number of infected CD4<sup>+</sup> T cells with introduction of small time delay, and in addition, there also exists a natural time delay factor during the process of virus replication. With state feedback control of time delay, the bifurcating periodical oscillating phenomena is induced via Hopf bifurcation. Mathematically, with the geometrical criterion applied in the stability analysis of delay model, the critical threshold of Hopf bifurcation in multiple delay differential equations which satisfy the transversal condition is derived. By applying reduction dimensional method combined with the center manifold theory, the stability of the bifurcating periodical solution is analyzed by the perturbation near Hopf point.
基金National Natural Science Foundation of China (No.60674088)
文摘This paper offeres an exact study on the robust stability of a kind of combined integrating control system, and the robust stability belongs to the analysis of a kind of quasi-polynomial with two independent time delays. The parameters of stable space under time delay uncertainty are fixed after Rekasius transformation, and then a new cluster treatment of characteristic roots (CTCR) procedure is adopted to determine the stable space. By this strategy we find that the unstable space is not continuous and both Karitonov vertices theory and Edge theory are unable to be extended to quasi-polynomial under time delay uncertainty.
基金supported by the National Key R&D Program of China(Grant No.2022YFB3305600)the National Natural Science Foundation of China(Grant Nos.62103015,62141604)+1 种基金the Natural Science Foundation of Shaanxi Providence(Grant No.2023-JC-QN0654)the Fundamental Research Funds for Central Universities of China(Grant No.JKF-20240144)。
文摘This article investigates the asymptotic and finite-time synchronization of fractional-order multiplex neural networks with multiple delays.Initially,a novel extended Halanay-type inequality for fractional-order differential equations with multiple delays is developed.Based on this framework,conditions are derived to achieve asymptotic synchronization by designing adaptive control schemes.Subsequently,novel sufficient criteria for achieving finite-time synchronization are established by introducing a hybrid control protocol that incorporates the Lyapunov method,inequality techniques,and a reduction to absurdity approach.Furthermore,the settling time for synchronization is explicitly estimated.In addition,the proposed methods are extended to in-vestigate asymptotic and finite-time synchronization for fractional-order multiplex neural networks with delay-free.In particular,the results represent a significant extension of the corresponding cases for integer-order systems.Finally,numerical simulations are provided to verify the theoretical findings.These results offer valuable insights into the synchronization of fractional-order networks with multiple delays,paving the way for scalable and practical solutions in areas such as secure communication and cross-layer integration in neural networks.
基金supported by the National Key Basic Research Program (Grant No. 2011CB706804)the National Natural Science Foundation of China (Grant No. 50835004)the Ministry of Science and Technology of China (Grant No. 2010ZX04016-012)
文摘This paper analyzes the stability of milling with variable pitch cutter and tool runout cases characterized by multiple delays,and proposes a new variable-step numerical integration method for efficient and accurate stability prediction. The variable-step technique is emphasized here to expand the numerical integration method,especially for the low radial immersion cases with multiple delays. First,the calculation accuracy of the numerical integration method is discussed and the variable-step algorithm is developed for milling stability prediction for single-delay and multiple-delay cases,respectively. The milling stability with variable pitch cutter is analyzed and the result is compared with those predicted with the frequency domain method and the improved full-discretization method. The influence of the runout effect on the stability boundary is investigated by the presented method. The numerical simulation shows that the cutter runout effect increases the stability boundary,and the increasing stability limit is verified by the milling chatter experimental results in the previous research. The numerical and experiment results verify the validity of the proposed method.
基金supported by the National Natural Science Foundation of China(Grant No.11302126)the State Key Program of National Natural Science of China(Grant No.11032009)+1 种基金the Shanghai Leading Academic Discipline Project(Grant No.B302)Young Teacher Training Program of Colleges and Universities in Shanghai(Grant No.ZZhy12030)
文摘In this paper,we investigate an inertial two-neural coupling system with multiple delays.We analyze the number of equilibrium points and demonstrate the corresponding pitchfork bifurcation.Results show that the system has a unique equilibrium as well as three equilibria for different values of coupling weights.The local asymptotic stability of the equilibrium point is studied using the corresponding characteristic equation.We find that multiple delays can induce the system to exhibit stable switching between the resting state and periodic motion.Stability regions with delay-dependence are exhibited in the parameter plane of the time delays employing the Hopf bifurcation curves.To obtain the global perspective of the system dynamics,stability and periodic activity involving multiple equilibria are investigated by analyzing the intersection points of the pitchfork and Hopf bifurcation curves,called the Bogdanov-Takens(BT)bifurcation.The homoclinic bifurcation and the fold bifurcation of limit cycle are obtained using the BT theoretical results of the third-order normal form.Finally,numerical simulations are provided to support the theoretical analyses.
基金supported by the Defense Industrial Development Program of China under Grant No.JCKY2017212C005
文摘This paper is concerned with the consensus problems for second-order multi-agent systems with multiple input delays.Different from all standard consensus algorithms with uniform delays,the authors aim to find the largest input-delay margin which can guarantee the consensus for the case when delays are nonuniform.Based on frequency domain analysis and matrix theory,an upper bound for maximum tolerable input-delay is given in terms of the relationship with scaling strengths and largest eigenvalue of the Lapalician matrix.Simulation results are provided to illustrate the obtained results.
文摘A system of delay differential equations is studied which represent a model for four neurons with time delayed connections between the neurons and time delayed feedback from each neuron to itself. The linear stability and bifurcation of the system are studied in a parameter space consisting of the sum of the time delays between the elements and the product of the strengths of the connections between the elements. Meanwhile, the bifurcation set are drawn in the parameter space.
基金supported by the National Natural Science Foundation of China(Grant Nos.11202068&11572224)the University Key Teacher Foundation for Youths of Henan Province(Grant No.2014GGJS-076)the Key Technologies Research Project of Henan Province(Grant No.152102210089)
文摘A coupled neural system with multiple delays has been investigated. The number of equilibrium points is analyzed. It implies that the neural system exhibits a unique equilibrium and three ones for the different values of coupling weight by employing the pitchfork bifurcation of the trivial equilibrium point. Further, the local asymptotical stability of the trivial equilibrium point is studied by analyzing the corresponding characteristic equation. Some stability criteria involving multiple delays and coupling weight are obtained. The results show that the neural system exhibits the delay-independent and delay-dependent stability. Increasing delay induces stability switching between resting state and periodic motion in some parameter regions of coupling weight. In addition, the criterion for the global stability of the trivial equilibrium is also derived by constructing a suitable Lyapunov functional. Finally, some numerical simulations are taken to support the theoretical results.
文摘The object of this article is to study the consequences of occurrence both fault in input and multiple time-varying delays simultaneously while designing observer to estimate the states of agents and also unknown nonlinear fault of system.Two delay dependent criteria are established to show the states of observer reach to states of MAS and also states of observer reach to consensus.From two obtained criteria,it can be deduced,by constructing a distributed controller-based observer design,MAS reach to consensus exponentially.Finally,the advantages of the obtained results are shown by solving an illustrative example.
