Generalized-Type Multistability of Almost Periodic Solutions for Memristive Cohen–Grossberg Neural Networks
Song Zhu, Yuanchu Shen, Chaoxu Mu, Xiaoyang Liu, Shiping Wen
Abstract
This article investigates a generalized type of multistability about almost periodic solutions for memristive Cohen–Grossberg neural networks (MCGNNs). As the inevitable disturbances in biological neurons, almost periodic solutions are more common in nature than equilibrium points (EPs). They are also generalizations of EPs in mathematics. According to the concepts of almost periodic solutions and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Psi$</tex-math> </inline-formula> -type stability, this article presents a generalized-type multistability definition of almost periodic solutions. The results show that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(K+1)^n$</tex-math> </inline-formula> generalized stable almost periodic solutions can coexist in a MCGNN with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$</tex-math> </inline-formula> neurons, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$</tex-math> </inline-formula> is a parameter of the activation functions. The enlarged attraction basins are also estimated based on the original state space partition method. Some comparisons and convincing simulations are given to verify the theoretical results at the end of this article.