By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural ...By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural networks subject to almost periodic external stimuli. Irt this paper, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures.展开更多
The global exponentially stability and the existence of periodic solutions of a class of Hopfield neural networks with time delays are investigated. By constructing a novel Lyapunov function, new criteria are provided...The global exponentially stability and the existence of periodic solutions of a class of Hopfield neural networks with time delays are investigated. By constructing a novel Lyapunov function, new criteria are provided to guarantee the global exponentially stability of such systems. For the delayed Hopfield neural networks with time-varying external inputs, new criteria are also acquired for the existence and exponentially stability of periodic solutions. The results are generalizations and improvements of some recent achievements reported in the literature on networks with time delays.展开更多
Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neur...Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neural network with periodic inputs are given by using Mawhin's coincidence degree theory and Liapunov's function method.展开更多
In this paper, a class of fuzzy BAM neural networks with time varying delays is discussed. By using the properties of M-matrix, Linear Matrix Inequality（LMI） approach and general Lyapunov-Krasovskii functional, some...In this paper, a class of fuzzy BAM neural networks with time varying delays is discussed. By using the properties of M-matrix, Linear Matrix Inequality（LMI） approach and general Lyapunov-Krasovskii functional, some new sufficient conditions are derived to ensure the existence of periodic solutions and the global exponential stability of the fuzzy BAM neural networks with time varying delays. These results have important significance in the design of global exponential stable BAM networks with delays. Moreover, an example is given to illustrate that the conditions of the results in the paper are feasible.展开更多
This paper considers a class of quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage delays.By utilizing the exponential dichotomy of linear differential equations,Banach’s fixed poin...This paper considers a class of quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage delays.By utilizing the exponential dichotomy of linear differential equations,Banach’s fixed point theorem and differential inequality techniques,the authors obtain some sufficient conditions to ensure the existence and global exponential stability of almost automorphic solutions for this class of quaternion-valued neural networks.The results are completely new.Finally,the authors give an example to illustrate the feasibility of the results.展开更多
A set of criteria are presented for the global exponential stability and the existence of periodic solutions of delayed cellular neural networks (DCNNs) by constructing suitable Lyapunov function-als, introducing many...A set of criteria are presented for the global exponential stability and the existence of periodic solutions of delayed cellular neural networks (DCNNs) by constructing suitable Lyapunov function-als, introducing many parameters qij* , rij* , qij, rij∈ R and wi】0 (i, j = 1, 2, …, n) and combining them with the elementary inequality 2ab≤a2 + b2 technique. These criteria have important significance in the design and applications of globally stable DCNNs and periodic oscillatory DCNNs. In addition, the results in literature are extended and improved. Two examples are given to illustrate the theory.展开更多
In this paper,using the continuation theorem of coincidence degree theory,Lyapu- nov functionals and some new inequality techniques,some new sufficient criteria are obtained to ensure the existence and global exponent...In this paper,using the continuation theorem of coincidence degree theory,Lyapu- nov functionals and some new inequality techniques,some new sufficient criteria are obtained to ensure the existence and global exponential stability of periodic solution. Our results are less restrictive than previous works and more effective than those in [12],which plays a significant role in designing globally exponentially stable and peri- odic oscillatory BAM neural networks with periodic coefficients.One example is also presented to demonstrate the advantages of our results.展开更多
基金The Soft Project (B30145) of Science and Technology of Hunan Province.
文摘By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural networks subject to almost periodic external stimuli. Irt this paper, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures.
基金the Science Foundation of Guangdong Province in China
文摘The global exponentially stability and the existence of periodic solutions of a class of Hopfield neural networks with time delays are investigated. By constructing a novel Lyapunov function, new criteria are provided to guarantee the global exponentially stability of such systems. For the delayed Hopfield neural networks with time-varying external inputs, new criteria are also acquired for the existence and exponentially stability of periodic solutions. The results are generalizations and improvements of some recent achievements reported in the literature on networks with time delays.
文摘Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neural network with periodic inputs are given by using Mawhin's coincidence degree theory and Liapunov's function method.
基金Supported by the National Natural Science Foundation of China (60574043)the Science Foundation of the Education Committee of Hunan Province (06C792+1 种基金07C700)the Construction Program of Key Disciplines in Hunan Province,Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan province
文摘In this paper, a class of fuzzy BAM neural networks with time varying delays is discussed. By using the properties of M-matrix, Linear Matrix Inequality（LMI） approach and general Lyapunov-Krasovskii functional, some new sufficient conditions are derived to ensure the existence of periodic solutions and the global exponential stability of the fuzzy BAM neural networks with time varying delays. These results have important significance in the design of global exponential stable BAM networks with delays. Moreover, an example is given to illustrate that the conditions of the results in the paper are feasible.
基金supported by the National Natural Sciences Foundation of People’s Republic of China under Grants Nos.11861072 and 11361072.
文摘This paper considers a class of quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage delays.By utilizing the exponential dichotomy of linear differential equations,Banach’s fixed point theorem and differential inequality techniques,the authors obtain some sufficient conditions to ensure the existence and global exponential stability of almost automorphic solutions for this class of quaternion-valued neural networks.The results are completely new.Finally,the authors give an example to illustrate the feasibility of the results.
文摘A set of criteria are presented for the global exponential stability and the existence of periodic solutions of delayed cellular neural networks (DCNNs) by constructing suitable Lyapunov function-als, introducing many parameters qij* , rij* , qij, rij∈ R and wi】0 (i, j = 1, 2, …, n) and combining them with the elementary inequality 2ab≤a2 + b2 technique. These criteria have important significance in the design and applications of globally stable DCNNs and periodic oscillatory DCNNs. In addition, the results in literature are extended and improved. Two examples are given to illustrate the theory.
基金This work was supported by the National Science Foundation of Hunan Provincial Education Department (05A057,06C792 and 07C700).
文摘In this paper,using the continuation theorem of coincidence degree theory,Lyapu- nov functionals and some new inequality techniques,some new sufficient criteria are obtained to ensure the existence and global exponential stability of periodic solution. Our results are less restrictive than previous works and more effective than those in [12],which plays a significant role in designing globally exponentially stable and peri- odic oscillatory BAM neural networks with periodic coefficients.One example is also presented to demonstrate the advantages of our results.
