Multistability of Almost Periodic Solution for Memristive Cohen-Grossberg Neural Networks With Mixed Delays

• Published in: IEEE transaction on neural networks and learning systems Vol. 31; no. 6; pp. 1914 - 1926
• Main Authors: Qin, Sitian, Ma, Qiang, Feng, Jiqiang, Xu, Chen
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.06.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Activation; Almost periodic solution; Artificial neural networks; Delays; Learning systems; memristive Cohen–Grossberg neural networks (MCGNNs); Memristors; mixed delays; multistability; Neural networks; Neurons; Stability analysis
• ISSN: 2162-237X; 2162-2388
• DOI: 10.1109/TNNLS.2019.2927506

This paper presents the multistability analysis of almost periodic state solutions for memristive Cohen-Grossberg neural networks (MCGNNs) with both distributed delay and discrete delay. The activation function of the considered MCGNNs is generalized to be nonmonotonic and nonpiecewise linear. It is shown that the MCGNNs with <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula>-neuron have <inline-formula> <tex-math notation="LaTeX">(K+1)^{n} </tex-math></inline-formula> locally exponentially stable almost periodic solutions, where nature number <inline-formula> <tex-math notation="LaTeX">K </tex-math></inline-formula> depends on the geometrical structure of the considered activation function. Compared with the previous related works, the number of almost periodic state solutions of the MCGNNs is extensively increased. The obtained conclusions in this paper are also capable of studying the multistability of equilibrium points or periodic solutions of the MCGNNs. Moreover, the enlarged attraction basins of attractors are estimated based on original partition. Some comparisons and convincing numerical examples are provided to substantiate the superiority and efficiency of obtained results.