Monostability and Multistability for Almost-Periodic Solutions of Fractional-Order Neural Networks With Unsaturating Piecewise Linear Activation Functions

• Published in: IEEE transaction on neural networks and learning systems Vol. 31; no. 12; pp. 5138 - 5152
• Main Authors: Wan, Peng, Sun, Dihua, Zhao, Min, Zhao, Hang
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.12.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Almost-periodic solution; Fractional calculus; fractional-order; Invariants; Mittag-Leffler attractive set; multistability; Neural networks; Stability analysis; Trajectory
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2020.2964030

Since the unsaturating activation function is unbounded, more complex dynamics may exist in neural networks with this kind of activation function. In this article, monostability and multistability results of almost-periodic solutions are developed for fractional-order neural networks with unsaturating piecewise linear activation functions. Some globally Mittag-Leffler attractive sets are given, and the existence of globally Mittag-Leffler stable almost-periodic solution is demonstrated by using Ascoli-Arzela theorem. In particular, some sufficient conditions are provided to ascertain the multistability of almost-periodic solutions based on locally positively invariant set. It shows that there exists an almost-periodic solution in each positively invariant set, and all trajectories converge to this periodic trajectory in that rectangular area. Two illustrative examples are provided to demonstrate the effectiveness of the proposed sufficient criteria.