Udhayakumar K, Rihan FA, Rakkiyappan R, Cao J. Fractional-order discontinuous systems with indefinite LKFs: An application to fractional-order neural networks with time delays.
Neural Netw 2021;
145:319-330. [PMID:
34798343 DOI:
10.1016/j.neunet.2021.10.027]
[Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2021] [Revised: 09/16/2021] [Accepted: 10/29/2021] [Indexed: 11/18/2022]
Abstract
In this article, we discuss bipartite fixed-time synchronization for fractional-order signed neural networks with discontinuous activation patterns. The Filippov multi-map is used to convert the fixed-time stability of the fractional-order general solution into the zero solution of the fractional-order differential inclusions. On the Caputo fractional-order derivative, Lyapunov-Krasovskii functional is proved to possess the indefinite fractional derivatives for fixed-time stability of fragmentary discontinuous systems. Furthermore, the fixed-time stability of the fractional-order discontinuous system is achieved as well as an estimate of the new settling time.. The discontinuous controller is designed for the delayed fractional-order discontinuous signed neural networks with antagonistic interactions and new conditions for permanent fixed-time synchronization of these networks with antagonistic interactions are also provided, as well as the settling time for permanent fixed-time synchronization. Two numerical simulation results are presented to demonstrate the effectiveness of the main results.
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