Existence and stability of periodic solutions for Hopfield neural network equations with periodic input

Boundedness and global stability for nonautonomous recurrent neural networks with distributed delays

“…We see that there have been considerable research on the nonautonomous neural networks (for example [27][28][29][30][31]). Particularly, in [27,28,31], the periodic Hopfield neural networks, cellular neural networks and BAM neural networks with variable coefficients and finite delays have been studied.…”

“…Particularly, in [27,28,31], the periodic Hopfield neural networks, cellular neural networks and BAM neural networks with variable coefficients and finite delays have been studied. By using the continuation theorem and Lyapunov functional method, the authors established some sufficient conditions to ensure the existence, uniqueness and global stability of periodic solutions.…”

On affine state-space neural networks for system identification: Global stability conditions and complexity management

“…Matrices A, B, C, D and E are real-valued matrices of appropriate dimensions, while the nonlinear activation function sðÁÞ is a continuous and differentiable sigmoidal function, upper and lower bounded satisfying the following conditions (Dong, Matsui, & Huang, 2002):…”

Convergence behavior of delayed cellular neural networks without periodic coefficients

“…Since CNN (3.1) is a very simple form of a delayed neural networks without periodic coefficients, therefore all the results in [2][3][4][5][6][7][8] and the references therein are not applicable for proving that all solutions of system (3.1) converge to a periodic function. This implies that the results of this work are essentially new.…”

“…In particular, extensive results on the problem of the existence and stability of periodic solutions for system (1.1) are given in many literature entries. We refer the reader to [2][3][4][5][6][7][8] and the references cited therein. Suppose that (H 0 ) c i , I i , a i j , b i j : R → R are continuous periodic functions, where i, j = 1, 2, .…”