The stability of a class of delayed cellular neural networks (DCNN) with or without noise perturbation is studied. After presenting a simple and easily checkable condition for the global exponential stability of a d...The stability of a class of delayed cellular neural networks (DCNN) with or without noise perturbation is studied. After presenting a simple and easily checkable condition for the global exponential stability of a deterministic system, we further investigate the case with noise perturbation. When DCNN is perturbed by external noise, the system is globally stable. An important fact is that, when the system is perturbed by internal noise, it is globally exponentially stable only if the total noise strength is within a certain bound. This is significant since the stochastic resonance phenomena have been found to exist in many nonlinear systems.展开更多
In this paper, almost sure exponential stability of neutral delayed cellular neural networks which are in the noised environment is studied by decomposing the state space to sub-regions in view of the saturation linea...In this paper, almost sure exponential stability of neutral delayed cellular neural networks which are in the noised environment is studied by decomposing the state space to sub-regions in view of the saturation linearity of output functions of neurons of the cellular neural networks. Some algebraic criteria are obtained and easily verified. Some examples are given to illustrate the correctness of the results obtained.展开更多
The exponential stability of the delayed cellular neural networks (DCNN's) is investigated. By dividing the network state variables into some parts according to the characters of the neural networks, some new suffi...The exponential stability of the delayed cellular neural networks (DCNN's) is investigated. By dividing the network state variables into some parts according to the characters of the neural networks, some new sufficient conditions of exponential stability are derived via constructing a Liapunov function. It is shown that the conditions differ from previous ones. The new conditions, which are associated with some initial value, are represented by some blocks of the interconnection matrix.展开更多
Some sufficient conditions for the global exponential stability and lower bounds on the rate of exponential convergence of the cellular neural networks with delay (DCNNs) are obtained by means of a method based on del...Some sufficient conditions for the global exponential stability and lower bounds on the rate of exponential convergence of the cellular neural networks with delay (DCNNs) are obtained by means of a method based on delay differential inequality. The method, which does not make use of any Lyapunov functional, is simple and valid for the stability analysis of neural networks with delay. Some previously established results in this paper are shown to be special casses of the presented result.展开更多
A new sufficient conditions for the global exponential stability of the equilibrium point for delayed cellular neural networks (DCNNs) is presented. It is shown that the use of a more general type of Lyapunov-Krasov...A new sufficient conditions for the global exponential stability of the equilibrium point for delayed cellular neural networks (DCNNs) is presented. It is shown that the use of a more general type of Lyapunov-Krasovskii function enables the derivation of new results for an exponential stability of the equilibrium point for DCNNs. The results establish a relation between the delay time and the parameters of the network. The results are also compared with one of the most recent results derived in the literature.展开更多
A global asymptotic stability problem of cellular neural networks with delay is investigated. A new stability condition is presented based on the Lyapunov-Krasovskii method, which is dependent on the amount of delay. ...A global asymptotic stability problem of cellular neural networks with delay is investigated. A new stability condition is presented based on the Lyapunov-Krasovskii method, which is dependent on the amount of delay. A result is given in the form of a linear matrix inequality, and the admitted upper bound of the delay can be easily obtained. The time delay dependent and independent results can be obtained, which include some previously published results. A numerical example is given to show the effectiveness of the main results.展开更多
The cellular neural networks with delay (DCNN’s) are investigated, and some new sufficient conditions on asymptotical stability of DCNN’s are derived by constructing the Liapunov functional and utilizing M ? matrixa...The cellular neural networks with delay (DCNN’s) are investigated, and some new sufficient conditions on asymptotical stability of DCNN’s are derived by constructing the Liapunov functional and utilizing M ? matrixand theω?limit set. It is shown that the new conditions are not related to the delayed parameter.展开更多
In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generaliz...In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.展开更多
This paper investigates the exponential stability of traveling wave solutions for nonlinear delayed cellular neural networks.As a continuity of the past work(Wu and Niu,2016;Yu,et al.,2011)on the existence and uniquen...This paper investigates the exponential stability of traveling wave solutions for nonlinear delayed cellular neural networks.As a continuity of the past work(Wu and Niu,2016;Yu,et al.,2011)on the existence and uniqueness of the traveling wave solutions,it is very reasonable and interesting to consider the exponential stability of the traveling wave solutions.By the weighted energy method,comparison principle and the first integral mean value theorem,this paper proves that,for all monotone traveling waves with the wave speed c<c1*<0 or c>c2*>0,the solutions converge time-exponentially to the corresponding traveling waves,when the initial perturbations decay at some fields.展开更多
基金the National Natural Science Foundation of China(No.10771155)the Special Foundation for the Authors of National Excellent Doctoral Dissertations of China(FANEDD)
文摘The stability of a class of delayed cellular neural networks (DCNN) with or without noise perturbation is studied. After presenting a simple and easily checkable condition for the global exponential stability of a deterministic system, we further investigate the case with noise perturbation. When DCNN is perturbed by external noise, the system is globally stable. An important fact is that, when the system is perturbed by internal noise, it is globally exponentially stable only if the total noise strength is within a certain bound. This is significant since the stochastic resonance phenomena have been found to exist in many nonlinear systems.
基金the National Natural Science Foundation of China (No. 10571036)Tianjin Municipal Education Commission of China(No. 20070405)
文摘In this paper, almost sure exponential stability of neutral delayed cellular neural networks which are in the noised environment is studied by decomposing the state space to sub-regions in view of the saturation linearity of output functions of neurons of the cellular neural networks. Some algebraic criteria are obtained and easily verified. Some examples are given to illustrate the correctness of the results obtained.
基金Supported by the National Natural Science Foundation of China (No.90208003, 30200059) and the Science and Technology Research Foundation of Education Ministry of China (No.02065)
文摘The exponential stability of the delayed cellular neural networks (DCNN's) is investigated. By dividing the network state variables into some parts according to the characters of the neural networks, some new sufficient conditions of exponential stability are derived via constructing a Liapunov function. It is shown that the conditions differ from previous ones. The new conditions, which are associated with some initial value, are represented by some blocks of the interconnection matrix.
文摘Some sufficient conditions for the global exponential stability and lower bounds on the rate of exponential convergence of the cellular neural networks with delay (DCNNs) are obtained by means of a method based on delay differential inequality. The method, which does not make use of any Lyapunov functional, is simple and valid for the stability analysis of neural networks with delay. Some previously established results in this paper are shown to be special casses of the presented result.
基金This project was supported in part by the National Natural Science Foundation of China (60404022, 60604004)the Key Scientific Research project of Education Ministry of China (204014)the National Natural Science Foundation of China for Distinguished Young Scholars (60525303).
文摘A new sufficient conditions for the global exponential stability of the equilibrium point for delayed cellular neural networks (DCNNs) is presented. It is shown that the use of a more general type of Lyapunov-Krasovskii function enables the derivation of new results for an exponential stability of the equilibrium point for DCNNs. The results establish a relation between the delay time and the parameters of the network. The results are also compared with one of the most recent results derived in the literature.
基金Project supported by the National Natural Science Foundation of China (No.60604004)the Natural Science Foundation of Hebei Province of China (No.F2007000637)the National Natural Science Foundation for Distinguished Young Scholars (No.60525303)
文摘A global asymptotic stability problem of cellular neural networks with delay is investigated. A new stability condition is presented based on the Lyapunov-Krasovskii method, which is dependent on the amount of delay. A result is given in the form of a linear matrix inequality, and the admitted upper bound of the delay can be easily obtained. The time delay dependent and independent results can be obtained, which include some previously published results. A numerical example is given to show the effectiveness of the main results.
基金Supported by the the National Natural Science Foundation of China (No.90208003, 30200059) and the Science and Technology Research Foundation of Education Ministry of China (No.02065)
文摘The cellular neural networks with delay (DCNN’s) are investigated, and some new sufficient conditions on asymptotical stability of DCNN’s are derived by constructing the Liapunov functional and utilizing M ? matrixand theω?limit set. It is shown that the new conditions are not related to the delayed parameter.
文摘In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.
基金supported by the Natural Science Foundation of Shandong Province under Grant No.ZR2017MA045the National Natural Science Foundation of China under Grant No.61873144。
文摘This paper investigates the exponential stability of traveling wave solutions for nonlinear delayed cellular neural networks.As a continuity of the past work(Wu and Niu,2016;Yu,et al.,2011)on the existence and uniqueness of the traveling wave solutions,it is very reasonable and interesting to consider the exponential stability of the traveling wave solutions.By the weighted energy method,comparison principle and the first integral mean value theorem,this paper proves that,for all monotone traveling waves with the wave speed c<c1*<0 or c>c2*>0,the solutions converge time-exponentially to the corresponding traveling waves,when the initial perturbations decay at some fields.