Existence and global exponential stability of periodic solution of a cellular neural networks difference equation with delays and impulses

Almost Periodic Solutions of Impulsive Integro‐differential Neural Networks

“…The reader can easily realize, nevertheless, that most of equations of models considered in the above mentioned papers are subject to periodic assumptions and the authors, in particular, studied the existence of their periodic solutions, see also [11,13,18,37,42]. On the other hand, upon considering long-term dynamical behaviors it is possible for the various components of the model to be periodic with rationally independent periods, and therefore it is more reasonable to consider the various parameters of models to be changing almost-periodically rather than periodically with a common period.…”

Asymptotic Behavior of Impulsive Infinite Delay Difference Equations with Continuous Variables

“…Recently, impulsive difference equations with discrete variable have attracted considerable attention. In particular, delay effect on the asymptotic behavior and other behaviors of impulsive difference equations with discrete variable has been extensively studied by many authors and various results are reported [8][9][10][11][12] . However, to the best of our knowledge, very little has been done with the corresponding problems for impulsive delay difference equations with continuous variables.…”

Multiplicity of positive periodic solutions for delayed difference equation with impulses

“…However, for the periodic problem of nonlinear functional difference equations, only in recent years there have been some research activities due to the realization that nonlinear functional difference equations are important in applications [1][2][3][4][5][6][7]. In [8], Wan and Jiang studied the general functional differential equation without impulsė…”

“…In numerical simulation and practical implementation of a differential equation, it is essential to formulate a discrete-time system that is an analogue of the continuous-time system [2]. We note that in practice, the dynamics of discrete-time systems may be quite different from those of continuous-time ones.…”

“…We note that in practice, the dynamics of discrete-time systems may be quite different from those of continuous-time ones. In particular, the existence criteria of periodic solution established for continuous-time systems with delays and impulses are not necessarily applicable to discrete-time systems [2]. Therefore, it is of both theoretical and practical importance to study the existence of periodic solution for functional difference equations with delays and impulses.…”