Boundedness and stability for nonautonomous cellular neural networks with delay

Coexistence of 2N domains of attraction of nonautonomous neural networks with time-varying delays

“…Particularly, when system (1.1) degenerates into periodic (autonomous) neural system, our results can be extended to the convergence dynamics of 2 N periodic orbits (equilibria) of system (1.1). Our results not only include related results in [31,33] but also extend results in [12][13][14][16][17][18][19][20] to the coexistence of domains of attraction.…”

“…In addition, convergence analysis of neural networks with delays is very important in theoretical research and there are considerable researches on the nonautonomous neural networks. For example, the general neural networks with variable coefficients and time-varying delays are studies in [16,[18][19][20][27][28][29], by using Lyapunov functional method, the continuation theorem, the techniques of matrix analysis and inequality analysis, the authors established a series of criteria on the boundedness, global exponential stability and the existence of periodic solutions. It is worth noting that the coexistence of multiple stable equilibria or periodic orbits is also very important in the applications of neural networks to pattern recognitions.…”

“…So in this paper, we consider the following nonautonomous neural networks with time-varying delays [17][18][19][20] . .…”

Global exponential stability of a class of neural networks with unbounded delays

“…According to [13], system (15) has a unique equilibrium point for any function g ∈ P L I and any input vector I if and only if -( A + B + C ) ∈ P 0 . Hence, Corollary 3 follows from Theorem 1.…”

“…The stability of nonautonomous cellular neural networks has been studied in [2,3,12,13]. However, results about the stability of neural networks with variable and unbounded delays and time-varying coefficients have not been widely studied.…”