Stability and pinning synchronization of delayed memristive neural networks with fractional-order and reaction-diffusion terms

Xiang Wu; Shutang Liu; Huiyu Wang; Yin Wang

doi:10.1016/j.isatra.2022.10.046

Stability and pinning synchronization of delayed memristive neural networks with fractional-order and reaction-diffusion terms

ISA Trans. 2023 May:136:114-125. doi: 10.1016/j.isatra.2022.10.046. Epub 2022 Nov 9.

Authors

Xiang Wu¹, Shutang Liu², Huiyu Wang³, Yin Wang⁴

Affiliations

¹ School of Control Science and Technology, Shandong University, Jinan, 250061, PR China. Electronic address: M_r_wrong@163.com.
² School of Control Science and Technology, Shandong University, Jinan, 250061, PR China. Electronic address: stliu@sdu.edu.cn.
³ School of Control Science and Technology, Shandong University, Jinan, 250061, PR China. Electronic address: huiyuwang001@163.com.
⁴ Institute of Marine Science and Technology, Shandong University, Qingdao, 266237, PR China. Electronic address: sduwangyin@163.com.

PMID: 36396510
DOI: 10.1016/j.isatra.2022.10.046

Abstract

Global asymptotic stability and synchronization are explored in this paper for fractional delayed memristive neural networks with reaction-diffusion terms (FDRDMNNs) in sense of Riemann-Liouville. First, we introduce diffusion into the existing model of fractional delayed memristive neural networks. Next, in terms of Green's theorem and inequality technique, a less conservative criterion for the asymptotic stability of FDRDMNNs is given by endowing Lyapunov direct method. Then, the appropriate pinning feedback controllers and adaptive controllers are designed to achieve the synchronization of the FDRDMNNs, and two sufficient conditions for global asymptotic synchronization are acquired. In addition, the results based on algebraic inequalities enhance some existing ones. The numerical simulations finally verify the validity of the derived results.

Keywords: Fractional; Memristive; Pinning synchronization; Reaction–diffusion; Stability.