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Abstract: In this paper, by using the theory of calculus on time scales, contraction mapping principle and Liapunov functional method, some sufficient conditions are obtained to ensure the existence and global exponential stability of periodic solution to BAM neural network with delays on time scales. This paper unifies the periodic discrete-time and continuous-time BAM neural networks under the same framework. [Copyright &y& Elsevier]

Abstract: Some sufficient conditions are derived to ensure the global exponential stability of delayed bi-directional associative memory (BAM) neural network on time scale, using the time scale calculus theory and the Liapunov functional method. The conditions possess highly important significance and can be easily checked in practice by simple algebraic methods. This is the first time applying the time scale calculus theory to unify and improve discrete-time and continuous-time bi-directional associate memory neural network under the same framework. [Copyright &y& Elsevier]

Abstract: Some sufficient conditions are obtained for the global exponential stability of periodic solutions to periodic bi-directional Cohen–Grossberg neural networks involving distributed delays, by using the Lyapunov functional method and some analytical techniques. These results improve and generalize some previous works, and are helpful for designing a global exponential stable periodic bi-directional Cohen–Grossberg neural networks. [Copyright &y& Elsevier]

Abstract: In this Letter, several sufficient conditions are obtained for the almost periodic attractor of delayed neural networks with variable coefficients based on the theory of exponential dichotomy, Lyapunov method and Halanay inequality technique. Many previous results reported in the literature are extended or improved for neural networks with or without delays. The obtained results are helpful to design globally stable almost periodic oscillatory neural networks. A numerical example is also given in the end to show the feasibility of our results. [Copyright &y& Elsevier]

By using the continuation theorem of Mawhin''s coincidence degree theory, Lyapunov functional method and some analytical techniques, some sufficient conditions are obtained ensuring existence and global exponential stability of periodic solution of the self-connection BAM neural networks with periodic coefficients and delays. These results are more effective than the ones in [IEEE Trans. Circuits Systems 50 (2003) 1162] for some neural networks, which has an important leading significance in the designing globally exponentially stable and periodic oscillatory BAM neural networks with self-connection. [Copyright &y& Elsevier]

By using some analytic techniques, several simple criteria are derived for the global exponential stability of delayed bi-directional associative memory (BAM) neural networks. Our results throw off the usual assumption that the activation function is of bounded character. Exponential converging velocity indexes are provided, which depend on the transmission delays and system parameters. A numerical example is also given to show the correctness of our analysis. These results have an important instructional significance in the design of exponential stable delayed BAM circuits. [Copyright &y& Elsevier]

Several sufficient conditions are obtained ensuring the existence and global exponential stability of almost periodic solution for BAM neural networks with distributed delays based on fixed point method and some analysis technique. Some previous results are improved and extended in this Letter and an example is given to illustrate the conditions of our results are feasible. These results are helpful to design globally exponentially stable BAM networks with continuously distributed delays. [Copyright &y& Elsevier]

We obtain some results about the existence and the global exponential stability conditions for almost periodic solution of delayed cellular neural networks(DCNNs) with variable coefficients by using the Banach fixed point theorem and constructing suitable Lyapunov functionals. These results possess important significance in design and applications of global stable DCNNs and almost periodic oscillatory DCNNs. [ABSTRACT FROM AUTHOR]

By combining the theory of the exponential dichotomy and Liapunov function, we study the existence and attractivity of almost periodic solutions for cellular neural networks (CNNs) with distributed delays and variable coefficientsdxi/dt=−bi(t)xi(t)+∑j=1naij(t)fj(xj(t))+∑j=1nbij(t)fjμj∫0∞kij(u)xj(t−u) du+Ii(t).We obtain some sufficient conditions to ensure that for the networks there exists a unique almost periodic solution, and all its solutions converge to such an almost periodic solution. An example is given to illustrate that the conditions of our results are feasible. [Copyright &y& Elsevier]

Using the Banach fixed point theorem, we obtain a sufficient condition for the existence of almost periodic solution of shunting inhibitory cellular neural networks dxij/dt=−aijxij−∑lower limit Ckl∈Nr(i,j) Cijklfxkl(t−τ)xij+Lij(t), the global attractivity of SICNNs is also obtained. An example is given to illustrate that the condition of our results are feasible. [Copyright &y& Elsevier]