Discrete Analogue for a Class of Impulsive Cohen–Grossberg Neural Networks with Asynchronous Time-Varying Delays
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This paper presents the exponential stability preservation in simulations of an impulsive Cohen–Grossberg neural networks with asynchronous time delays. By semi-discrete technique and impulsive maps as discrete representations of the nonlinear impulsive networks, difference equations formulated is obtained. And developing a new delay impulsive discrete time differential inequality, several sufficient conditions are derived to guarantee the global exponential stability in Lagrange sense and exponential convergence in Lyapunov sense of the discussed discrete time delayed Cohen–Grossberg system. It is show that the discrete time technique can preserve the equilibrium point of the continuous time model. Finally, one numerical example with simulation shows the effectiveness of the obtained results.
KeywordsSemi-discretisation Exponential convergence Impulsive discrete time difference equations
The authors are grateful for the Scientific and Technological Research Program of Chongqing Municipal Education Commission(Grant Nos. KJ1710253, KJ1601002), the Youth Fund of Chongqing Three Gorges University(Grant No. 16QN14), and the support of the National Natural Science Foundation of China (61633011, 11601047), Project supported by Key Laboratory of Chongqing Municipal Institutions of Higher Education (Grant No. 3).