Multiple Mittag-Leffler Stability of Fractional-Order Recurrent Neural Networks

作者：Liu, Peng^*; Zeng, Zhigang; Wang, Jun

来源：IEEE Transactions on Systems, Man, and Cybernetics: Systems , 2017, 47(8): 2279-2288.

DOI：10.1109/TSMC.2017.2651059

• Fractional-order recurrent neural networks
• Mittag-Leffler stability
• multistability

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.

• 出版日期2017-8
• 单位华中科技大学; 武汉工程大学