Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays （RNNs） are studied. By employing the inequality α∏k=1^m ...Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays （RNNs） are studied. By employing the inequality α∏k=1^m bk^qk≤1/r ∑qkbk^r＋1/rα^r（α≥0,bk≥0,qk〉0,with ∑k=1^m qk=r-1,r≥1, constructing suitable Lyapunov r k=l k=l functions and applying the homeomorphism theory, a family of simple and new sufficient conditions are given ensuring the global exponential stability and the existence of periodic solutions of RNNs. The results extend and improve the results of earlier publications.展开更多
By using the properties of nonnegative matrices and techniques of differential inequalities,some sufficient conditions for the global exponential stability of cellular neural networks with time delays were obtained.Th...By using the properties of nonnegative matrices and techniques of differential inequalities,some sufficient conditions for the global exponential stability of cellular neural networks with time delays were obtained.The criteria do not require such conditions as boundedness and differentiability of activation functions.The conditions of the theorem were verified.展开更多
Finite-time stability of a class of fractional-order neural networks is investigated in this paper. By Laplace transform, the generalized Gronwa11 inequality and estimates of Mittag-Leffier functions, sufficient condi...Finite-time stability of a class of fractional-order neural networks is investigated in this paper. By Laplace transform, the generalized Gronwa11 inequality and estimates of Mittag-Leffier functions, sufficient conditions are pre- sented to ensure the finite-time stability of such neural models with the Caputo fractionM derivatives. Furthermore, results about asymptotical stability of fractional-order neural models are also obtained.展开更多
This paper is concerned with fractional-order bidirectional associative memory(BAM) neural networks with time delays. Applying Laplace transform, the generalized Gronwall inequality and estimates of Mittag–Leffler fu...This paper is concerned with fractional-order bidirectional associative memory(BAM) neural networks with time delays. Applying Laplace transform, the generalized Gronwall inequality and estimates of Mittag–Leffler functions, some sufficient conditions which ensure the finite-time stability of fractional-order bidirectional associative memory neural networks with time delays are obtained. Two examples with their simulations are given to illustrate the theoretical findings. Our results are new and complement previously known results.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 high-order neural networks with proportional delays. The proportional delay is a time-varying unbounded delay which is different from the constant delay, bounded time-varying delay and dis...This paper is concerned with high-order neural networks with proportional delays. The proportional delay is a time-varying unbounded delay which is different from the constant delay, bounded time-varying delay and distributed delay. By the nonlinear transformation yi(t) = ui( et)(i = 1, 2,..., n), we transform a class of high-order neural networks with proportional delays into a class of high-order neural networks with constant delays and timevarying coefficients. With the aid of Brouwer fixed point theorem and constructing the delay differential inequality, we obtain some delay-independent and delay-dependent sufficient conditions to ensure the existence, uniqueness and global exponential stability of equilibrium of the network. Two examples with their simulations are given to illustrate the theoretical findings. Our results are new and complement previously known results.展开更多
In this paper, we consider the existence, the uniqueness, the global exponential stability, the global asymptotic stability, the uniform asymptotic stability and the uniform stability of the equilibrium point of impul...In this paper, we consider the existence, the uniqueness, the global exponential stability, the global asymptotic stability, the uniform asymptotic stability and the uniform stability of the equilibrium point of impulsive competitive neural networks with distributed delays and leakage time-varying delays. The existence of a unique equilibrium point is proved by using Brouwer's fixed point theorem. By finding suitable Lyapunov-Krasovskii functional, some sufficient conditions are derived ensuring some kinds of stability. Finally, several examples and their simulations are given to illustrate the effectiveness of the obtained results.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
In this paper, we consider a Cohen-Grossberg neural network with three delays. Regard- ing time delays as a parameter, we investigate the effect of time delays on its dynamics. We show that there exist stability switc...In this paper, we consider a Cohen-Grossberg neural network with three delays. Regard- ing time delays as a parameter, we investigate the effect of time delays on its dynamics. We show that there exist stability switches for time delays under certain conditions and the conditions for the existence of periodic oscillations are given by discussing the associated characteristic equation. Numerical simulations are given to illustrate the obtained results and interesting network behaviors are observed, such as multiple stability switches of the network equilibrium and synchronous （asynchronous） oscillations.展开更多
In this paper, we study the existence, uniqueness and stability of memristor-based syn- chronous switching neural networks with time delays. Several criteria of exponential stability are given by introducing multiple ...In this paper, we study the existence, uniqueness and stability of memristor-based syn- chronous switching neural networks with time delays. Several criteria of exponential stability are given by introducing multiple Lyapunov functions. In comparison with the existing publications on simplice memristive neural networks or switching neural net- works, we consider a system with a series of switchings, these switchings are assumed to be synchronous with memristive switching mechanism. Moreover, the proposed stability conditions are straightforward and convenient and can reflect the impact of time delay on the stability. Two examples are also presented to illustrate the effectiveness of the theoretical results.展开更多
In the paper, the anti-synchronization problem of the general delayed chaotic neural networks is investigated. For the master and slave systems, we obtain a control law to achieve the state anti-synchronization of two...In the paper, the anti-synchronization problem of the general delayed chaotic neural networks is investigated. For the master and slave systems, we obtain a control law to achieve the state anti-synchronization of two identical chaotic neural networks. By using the Halanay inequality lemma and Lyapunov stability method, we derive a delay indepen- dent sufficient exponential anti-synchronization condition relative to the parameters of the systems and controller gain matrix. The condition is easily verified in practice. Finally, the theoretical results are applied to two delayed chaotic neural networks, and numerical simulations are given to demonstrate the performance of the proposed scheme throughout some examples.展开更多
文摘Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays （RNNs） are studied. By employing the inequality α∏k=1^m bk^qk≤1/r ∑qkbk^r＋1/rα^r（α≥0,bk≥0,qk〉0,with ∑k=1^m qk=r-1,r≥1, constructing suitable Lyapunov r k=l k=l functions and applying the homeomorphism theory, a family of simple and new sufficient conditions are given ensuring the global exponential stability and the existence of periodic solutions of RNNs. The results extend and improve the results of earlier publications.
基金the Foundation of Technology Project of Chongqing Education Commission (No. 041503)
文摘By using the properties of nonnegative matrices and techniques of differential inequalities,some sufficient conditions for the global exponential stability of cellular neural networks with time delays were obtained.The criteria do not require such conditions as boundedness and differentiability of activation functions.The conditions of the theorem were verified.
基金Supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.20093401120001the Natural Science Foundation of Anhui Province under Grant No.11040606M12+1 种基金the Natural Science Foundation of Anhui Education Bureau under Grant No.KJ2010A035the 211 Project of Anhui University under Grant No.KJJQ1102
文摘Finite-time stability of a class of fractional-order neural networks is investigated in this paper. By Laplace transform, the generalized Gronwa11 inequality and estimates of Mittag-Leffier functions, sufficient conditions are pre- sented to ensure the finite-time stability of such neural models with the Caputo fractionM derivatives. Furthermore, results about asymptotical stability of fractional-order neural models are also obtained.
基金Supported by National Natural Science Foundation of China under Grant Nos.61673008,11261010,11101126Project of High–Level Innovative Talents of Guizhou Province([2016]5651)+2 种基金Natural Science and Technology Foundation of Guizhou Province(J[2015]2025 and J[2015]2026)125 Special Major Science and Technology of Department of Education of Guizhou Province([2012]011)Natural Science Foundation of the Education Department of Guizhou Province(KY[2015]482)
文摘This paper is concerned with fractional-order bidirectional associative memory(BAM) neural networks with time delays. Applying Laplace transform, the generalized Gronwall inequality and estimates of Mittag–Leffler functions, some sufficient conditions which ensure the finite-time stability of fractional-order bidirectional associative memory neural networks with time delays are obtained. Two examples with their simulations are given to illustrate the theoretical findings. Our results are new and complement previously known results.
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 National Natural Science Foundation of China under Grant Nos.61673008 and 11261010Project of High-level Innovative Talents of Guizhou Province([2016]5651)
文摘This paper is concerned with high-order neural networks with proportional delays. The proportional delay is a time-varying unbounded delay which is different from the constant delay, bounded time-varying delay and distributed delay. By the nonlinear transformation yi(t) = ui( et)(i = 1, 2,..., n), we transform a class of high-order neural networks with proportional delays into a class of high-order neural networks with constant delays and timevarying coefficients. With the aid of Brouwer fixed point theorem and constructing the delay differential inequality, we obtain some delay-independent and delay-dependent sufficient conditions to ensure the existence, uniqueness and global exponential stability of equilibrium of the network. Two examples with their simulations are given to illustrate the theoretical findings. Our results are new and complement previously known results.
文摘In this paper, we consider the existence, the uniqueness, the global exponential stability, the global asymptotic stability, the uniform asymptotic stability and the uniform stability of the equilibrium point of impulsive competitive neural networks with distributed delays and leakage time-varying delays. The existence of a unique equilibrium point is proved by using Brouwer's fixed point theorem. By finding suitable Lyapunov-Krasovskii functional, some sufficient conditions are derived ensuring some kinds of stability. Finally, several examples and their simulations are given to illustrate the effectiveness of the obtained results.
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In this paper, we consider a Cohen-Grossberg neural network with three delays. Regard- ing time delays as a parameter, we investigate the effect of time delays on its dynamics. We show that there exist stability switches for time delays under certain conditions and the conditions for the existence of periodic oscillations are given by discussing the associated characteristic equation. Numerical simulations are given to illustrate the obtained results and interesting network behaviors are observed, such as multiple stability switches of the network equilibrium and synchronous （asynchronous） oscillations.
文摘In this paper, we study the existence, uniqueness and stability of memristor-based syn- chronous switching neural networks with time delays. Several criteria of exponential stability are given by introducing multiple Lyapunov functions. In comparison with the existing publications on simplice memristive neural networks or switching neural net- works, we consider a system with a series of switchings, these switchings are assumed to be synchronous with memristive switching mechanism. Moreover, the proposed stability conditions are straightforward and convenient and can reflect the impact of time delay on the stability. Two examples are also presented to illustrate the effectiveness of the theoretical results.
文摘In the paper, the anti-synchronization problem of the general delayed chaotic neural networks is investigated. For the master and slave systems, we obtain a control law to achieve the state anti-synchronization of two identical chaotic neural networks. By using the Halanay inequality lemma and Lyapunov stability method, we derive a delay indepen- dent sufficient exponential anti-synchronization condition relative to the parameters of the systems and controller gain matrix. The condition is easily verified in practice. Finally, the theoretical results are applied to two delayed chaotic neural networks, and numerical simulations are given to demonstrate the performance of the proposed scheme throughout some examples.
