Dynamical stability analysis of multiple equilibrium points in time-varying delayed recurrent neural networks with discontinuous activation functions

被引：67

作者：

Huang, Yujiao ^{[1
]}

Zhang, Huaguang ^{[1
]}

Wang, Zhanshan ^{[1
]}

机构：

[1] Northeastern Univ, Sch Informat Sci & Engn, Shenyang 110819, Liaoning, Peoples R China

来源：

NEUROCOMPUTING | 2012年 / 91卷

基金：

中国国家自然科学基金;

关键词：

Recurrent neural network; Discontinuous activation function; Multistability; ROBUST EXPONENTIAL STABILITY; GLOBAL CONVERGENCE; ASSOCIATIVE MEMORY; MULTISTABILITY; MULTIPERIODICITY; ATTRACTIVITY;

D O I：

10.1016/j.neucom.2012.02.016

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

This paper is concerned with the dynamical stability analysis of multiple equilibrium points in recurrent neural networks with time-varying delays and discontinuous activation functions. Based on the decomposition of state space, some sufficient conditions for the existence of multiple equilibrium points are established, which ensure that n-dimensional recurrent neural networks with k-level discontinuous activation functions can have k(n) equilibrium points. Under these conditions, the equilibrium points are locally exponentially stable. Moreover, some conditions for the existence of sets of stable equilibrium points and unstable equilibrium points are derived for recurrent neural networks without delay and with discontinuous activation functions. Finally, three examples are given to illustrate the effectiveness of the results. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：21 / 28

页数：8

共 50 条

[31] Global stability analysis of competitive neural networks with mixed time-varying delays and discontinuous neuron activations [J].

Wang, Yanqun ;

Huang, Lihong .

NEUROCOMPUTING, 2015, 152 :85-96

[32] Dynamical Behaviors of Multiple Equilibria in Competitive Neural Networks With Discontinuous Nonmonotonic Piecewise Linear Activation Functions [J].

Nie, Xiaobing ;

Zheng, Wei Xing .

IEEE TRANSACTIONS ON CYBERNETICS, 2016, 46 (03) :679-693

[33] Complete Stability of Delayed Recurrent Neural Networks With New Wave-Type Activation Functions [J].

Yan, Zepeng ;

Sun, Wen ;

Guo, Wanli ;

Li, Biwen ;

Wen, Shiping ;

Cao, Jinde .

IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2025, 36 (04) :6584-6596

[34] Robust Stability of Recurrent Neural Networks With Time-Varying Delays and Input Perturbation [J].

Zhang, Fanghai ;

Zeng, Zhigang .

IEEE TRANSACTIONS ON CYBERNETICS, 2021, 51 (06) :3027-3038

[35] Multiple O(t-q) stability and instability of time-varying delayed fractional-order Cohen-Grossberg neural networks with Gaussian activation functions [J].

Wan, Liguang ;

Liu, Zhenxing .

NEUROCOMPUTING, 2021, 454 :212-227

[36] Multiple μ-stability and multiperiodicity of delayed memristor-based fuzzy cellular neural networks with nonmonotonic activation functions [J].

Liu, Yunfeng ;

Song, Zhiqiang ;

Tan, Manchun .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2019, 159 :1-17

[37] Solubility and stability of recurrent neural networks with nonlinearity or time-varying delays [J].

Yen, Eva C. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2011, 16 (01) :509-521

[38] Global exponential periodicity and global exponential stability of a class of recurrent neural networks with various activation functions and time-varying delays [J].

Chen, Boshan ;

Wang, Jun .

NEURAL NETWORKS, 2007, 20 (10) :1067-1080

[39] An Overview of the Stability Analysis of Recurrent Neural Networks With Multiple Equilibria [J].

Liu, Peng ;

Wang, Jun ;

Zeng, Zhigang .

IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2023, 34 (03) :1098-1111

[40] Coexistence and local stability of multiple equilibrium points for fractional-order state-dependent switched competitive neural networks with time-varying delays [J].

Wu, Zhongwen ;

Nie, Xiaobing ;

Cao, Boqiang .

NEURAL NETWORKS, 2023, 160 :132-147

← 1 2 3 4 5 →