Journal
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
Volume 47, Issue 8, Pages 2279-2288Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSMC.2017.2651059
Keywords
Fractional-order recurrent neural networks; Mittag-Leffler stability; multistability
Funding
- Natural Science Foundation of China [61673188, 61673330]
- National Key Research and Development Program of China [2016YFB0800402]
- Science and Technology Support Program of Hubei Province [2015BHE013]
- Program for Changjiang Scholars and Innovative Research Team in University of China [IRT1245]
- Research Grants Council of the Hong Kong Special Administrative Region, China [14207614]
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In this paper, coexistence and stability of multiple equilibrium points of fractional-order recurrent neural networks are addressed. Several sufficient conditions are derived for ascertaining the existence of Pi(n)(i = 1)(2K(i) + 1) equilibrium points (K-i >= 0) and the local Mittag-Leffler stability of Pi(n)(i = 1)(K-i + 1) equilibrium points of them by using the geometrical properties of activation functions and algebraic properties of nonsingular M-matrix. In contrast with many existing results, the derived results cover both mono-stability and multistability, and the activation functions herein could be nonmonotonic and nonlinear in any open interval. In addition, three numerical examples are elaborated to substantiate the efficacy and characteristics of the theoretical results.
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