Multistability of S-Asymptotically ω-Periodic Solutions for Fractional-Order Neural Networks with Time Variable Delays

Abstract

This paper explores the multistability of S-asymptotically $\omega$-periodic solutions for fractional-order neural networks with time variable delays (FVDNNs). Benefited from the geometrical configuration of the nonlinear and non-monotonic activation function, we prove the coexistence of $(K+1)^{n}$ S-asymptotically $\omega$-periodic solutions with multiple asymptotical stability, where K is a positive integer. In contrast to the previous works, the obtained results extensively raise the amount of S-asymptotically $\omega$-periodic solutions of FVDNNs in this paper. Besides, two numerical examples are shown to illustrate the feasibility of obtained results.