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Periodic Solutions of Cohen-Grossberg-Type BAM Neural Networks with Time-Varying Delays  [PDF]
Qiming Liu, Shaoning Li
Int'l J. of Communications, Network and System Sciences (IJCNS) , 2012, DOI: 10.4236/ijcns.2012.512085
Abstract: Sufficient conditions to guarantee the existence and global exponential stability of periodic solutions of a Cohen-Grossberg-type BAM neural network are established by suitable mathematical transformation.
Periodic Solutions of a Cohen-Grossberg-Type BAM Neural Networks with Distributed Delays and Impulses
Qiming Liu,Rui Xu
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/643418
Abstract: A class of Cohen-Grossberg-type BAM neural networks with distributed delays and impulses are investigated in this paper. Sufficient conditions to guarantee the uniqueness and global exponential stability of the periodic solutions of such networks are established by using suitable Lyapunov function, the properties of -matrix, and some suitable mathematical transformation. The results in this paper improve the earlier publications.
Existence and Global Exponential Stability of Periodic Solution to Cohen-Grossberg BAM Neural Networks with Time-Varying Delays
Kaiyu Liu,Zhengqiu Zhang,Liping Wang
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/805846
Abstract: We investigate first the existence of periodic solution in general Cohen-Grossberg BAM neural networks with multiple time-varying delays by means of using degree theory. Then using the existence result of periodic solution and constructing a Lyapunov functional, we discuss global exponential stability of periodic solution for the above neural networks. Our result on global exponential stability of periodic solution is different from the existing results. In our result, the hypothesis for monotonicity ineqiality conditions in the works of Xia (2010) Chen and Cao (2007) on the behaved functions is removed and the assumption for boundedness in the works of Zhang et al. (2011) and Li et al. (2009) is also removed. We just require that the behaved functions satisfy sign conditions and activation functions are globally Lipschitz continuous.
具分布时滞双向Cohen-Grossberg模型的伪概周期解
Pseudo Almost Periodic Solution of Bidirectional Co-hen-Grossberg Neural Networks with Distributed Delays
 [PDF]

向红军, 魏叶梅, 王金华
Pure Mathematics (PM) , 2013, DOI: 10.12677/PM.2013.31006
Abstract:
利用不动点定理和不等式分析技巧,研究了一类具分布时滞的双向Cohen-Grossberg神经网络模型,得到了一个新的充分条件,确保该模型伪概周期解存在性与唯一性,最后用一个实例说明所得结论的正确性
In this paper, by using fixed point theorem and inequality techniques, a new sufficient condition is obtained to ensure the existence and unique for the pseudo almost periodic solution of a class bidirectional Cohen-Grossberg neural networks with distributed delays. An example is given to illustrate the correctness of our discussions.
Global Exponential Stability of Delayed Cohen-Grossberg BAM Neural Networks with Impulses on Time Scales  [cached]
Li Yongkun,Hua Yuchun,Fei Yu
Journal of Inequalities and Applications , 2009,
Abstract: Based on the theory of calculus on time scales, the homeomorphism theory, Lyapunov functional method, and some analysis techniques, sufficient conditions are obtained for the existence, uniqueness, and global exponential stability of the equilibrium point of Cohen-Grossberg bidirectional associative memory (BAM) neural networks with distributed delays and impulses on time scales. This is the first time applying the time-scale calculus theory to unify the discrete-time and continuous-time Cohen-Grossberg BAM neural network with impulses under the same framework.
Global Exponential Stability of Delayed Cohen-Grossberg BAM Neural Networks with Impulses on Time Scales
Yongkun Li,Yuchun Hua,Yu Fei
Journal of Inequalities and Applications , 2009, DOI: 10.1155/2009/491268
Abstract: Based on the theory of calculus on time scales, the homeomorphism theory, Lyapunov functional method, and some analysis techniques, sufficient conditions are obtained for the existence, uniqueness, and global exponential stability of the equilibrium point of Cohen-Grossberg bidirectional associative memory (BAM) neural networks with distributed delays and impulses on time scales. This is the first time applying the time-scale calculus theory to unify the discrete-time and continuous-time Cohen-Grossberg BAM neural network with impulses under the same framework.
Existence and attractivity of periodic solutions to Cohen-Grossberg neural network with distributed delays  [cached]
Yongkun Li,Lifei Zhu
Electronic Journal of Differential Equations , 2005,
Abstract: We study the existence and exponential attractivity of periodic solutions to Cohen-Grossberg neural network with distributed delays. Our results are obtained by applying the continuation theorem of coincidence degree theory and a general Halanay inequality.
Periodic Oscillation of Fuzzy Cohen-Grossberg Neural Networks with Distributed Delay and Variable Coefficients
Hongjun Xiang,Jinde Cao
Journal of Applied Mathematics , 2008, DOI: 10.1155/2008/453627
Abstract: A class of fuzzy Cohen-Grossberg neural networks with distributed delay and variable coefficients is discussed. It is neither employing coincidence degree theory nor constructing Lyapunov functionals, instead, by applying matrix theory and inequality analysis, some sufficient conditions are obtained to ensure the existence, uniqueness, global attractivity and global exponential stability of the periodic solution for the fuzzy Cohen-Grossberg neural networks. The method is very concise and practical. Moreover, two examples are posed to illustrate the effectiveness of our results.
Anti-periodic Solutions of Impulsive Cohen-Grossberg SICNNs on Time Scales  [cached]
Meng Hu,Lili Wang,Lili Wang
Journal of Mathematics Research , 2011, DOI: 10.5539/jmr.v3n1p131
Abstract: By using the method of coincidence degree and constructing suitable Lyapunov functional, some sufficient conditions are established for the existence and global exponential stability of anti-periodic solutions for a kind of impulsive Cohen- Grossberg shunting inhibitory cellular neural networks (CGSICNNs) on time scales. An example is given to illustrate our results.
Global Robust Exponential Stability and Periodic Solutions for Interval Cohen-Grossberg Neural Networks with Mixed Delays  [PDF]
Yanke Du,Rui Xu
Discrete Dynamics in Nature and Society , 2013, DOI: 10.1155/2013/963897
Abstract: A class of interval Cohen-Grossberg neural networks with time-varying delays and infinite distributed delays is investigated. By employing H-matrix and M-matrix theory, homeomorphism techniques, Lyapunov functional method, and linear matrix inequality approach, sufficient conditions are established for the existence, uniqueness, and global robust exponential stability of the equilibrium point and the periodic solution to the neural networks. Our results improve some previously published ones. Finally, numerical examples are given to illustrate the feasibility of the theoretical results and further to exhibit that there is a characteristic sequence of bifurcations leading to a chaotic dynamics, which implies that the system admits rich and complex dynamics. 1. Introduction In the past two decades, neural networks have received a great deal of attention due to the extensive applications in many areas such as signal processing, associative memory, pattern recognition, and parallel computation and optimization. It should be pointed out that the successful applications heavily rely on the dynamic behaviors of neural networks. Stability, as one of the most important properties of neural networks, is crucially required when designing neural networks. In electronic implementation of neural networks, there exist inevitably some uncertainties caused by the existence of modeling errors, external disturbance, and parameter fluctuation, which would lead to complex dynamic behaviors. Thus, it is important to investigate the robustness of neural networks against such uncertainties and deviations (see [1–8] and references therein). In [4–6], employing homeomorphism techniques, Lyapunov method, -matrix and -matrix theory, and linear matrix inequality (LMI) approach, Shao et al. established some sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point for the following interval Hopfield neural networks: where is time-varying delay which is variable with time due to the finite switching speed of amplifiers. Recently, the stability of neural networks with time-varying delays has been extensively investigated, and various sufficient conditions have been established for the global asymptotic and exponential stability in [9–13]. Generally, neural networks usually have a spatial extent due to the presence of a multitude of parallel pathways with a variety of axon sizes and lengths. It is desired to model them by introducing continuously distributed delays over a certain duration of time such that the distant past has
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