Generalized-Type Multistability of Almost Periodic Solutions for Memristive Cohen-Grossberg Neural Networks.

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 Ψ -type stability, this article presents a generalized-type multistability definition of almost periodic solutions. The results show that (K+1)n generalized stable almost periodic solutions can coexist in a MCGNN with n neurons, where K 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.

Multiple Mittag-Leffler Stability of Fractional-Order Complex-Valued Memristive Neural Networks With Delays.

This article discusses the coexistence and dynamical behaviors of multiple equilibrium points (Eps) for fractional-order complex-valued memristive neural networks (FCVMNNs) with delays. First, based on the state space partition method, some sufficient conditions are proposed to guarantee that there are multiple Eps in one FCVMNN. Then, the Mittag-Leffler stability of those multiple Eps is proved by using the Lyapunov function. Simultaneously, the enlarged attraction basins are obtained to improve and extend the existing theoretical results in the previous literature. In addition, some existing stability results in the literature are special cases of a new result herein. Finally, two illustrative examples with computer simulations are presented to verify the effectiveness of theoretical analysis.

Multistability and associative memory of neural networks with Morita-like activation functions.

This paper presents the multistability analysis and associative memory of neural networks (NNs) with Morita-like activation functions. In order to seek larger memory capacity, this paper proposes Morita-like activation functions. In a weakened condition, this paper shows that the NNs with n-neurons have (2m+1)n equilibrium points (Eps) and (m+1)n of them are locally exponentially stable, where the parameter m depends on the Morita-like activation functions, called Morita parameter. Also the attraction basins are estimated based on the state space partition. Moreover, this paper applies these NNs into associative memories (AMs). Compared with the previous related works, the number of Eps and AM's memory capacity are extensively increased. The simulation results are illustrated and some reliable associative memories examples are shown at the end of this paper.