Multiple O(t−α) stability for fractional-order neural networks with time-varying delays. Issue 17 (November 2020)

• Record Type: Journal Article
• Authors: Wan, Liguang; Liu, Zhenxing
• Is Part Of: Journal of the Franklin Institute. Volume 357:Issue 17(2020)
• Page Start: 12742
• Page End: 12766
• Publication Date: 2020-11
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2020.09.019
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: In this paper, the multiple O ( t − α ) stability for fractional-order neural networks (FoNNs) with time-varying delays is formulated and explored. According to n pairs of bounded functions, which are obtained from FoNNs model as well as the maximum and minimum values of the activation functions, state space is partitioned into ∏ i = 1 n ( 2 M i + 1 ) parts, where Mi ≥ 0 is a nonnegative integer and is determined by bounded functions. Sufficient conditions are acquired to guarantee the existence of ∏ i = 1 n ( M i + 1 ) O ( t − α ) stable equilibrium points. The obtained criteria generalize and extend the existing results. Several illustrative examples are raised to confirm the effectiveness of the theoretical results.