Fractional-order discontinuous systems with indefinite LKFs: An application to fractional-order neural networks with time delays

• Published in: Neural networks Vol. 145; pp. 319 - 330
• Main Authors: Udhayakumar, K., Rihan, Fathalla A., Rakkiyappan, R., Cao, Jinde
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01-01-2022
• Subjects: Algorithms; Computer Simulation; Discontinuous activations; Fixed-time synchronization; Fractional-order; Lyapunov-Krasovskii functional; Neural Networks, Computer; Signed neural networks; Time; Fixed-time synchronization; Discontinuous activations; Lyapunov-Krasovskii functional; Fractional-order; Signed neural networks
• ISSN: 0893-6080; 1879-2782
• DOI: 10.1016/j.neunet.2021.10.027

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