Exponential stability of a class of complex-valued neural networks with time-varying delays

2015 ◽  
Vol 164 ◽  
pp. 293-299 ◽  
Author(s):  
Jie Pan ◽  
Xinzhi Liu ◽  
Weichau Xie
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Time Varying ◽  
Complex Valued

scholarly journals Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaohui Xu ◽  
Jiye Zhang ◽  
Quan Xu ◽  
Zilong Chen ◽  
Weifan Zheng
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Time Varying ◽  
Homeomorphism Mapping ◽  
Complex Valued

This paper studies the global exponential stability for a class of impulsive disturbance complex-valued Cohen-Grossberg neural networks with both time-varying delays and continuously distributed delays. Firstly, the existence and uniqueness of the equilibrium point of the system are analyzed by using the corresponding property of M-matrix and the theorem of homeomorphism mapping. Secondly, the global exponential stability of the equilibrium point of the system is studied by applying the vector Lyapunov function method and the mathematical induction method. The established sufficient conditions show the effects of both delays and impulsive strength on the exponential convergence rate. The obtained results in this paper are with a lower level of conservatism in comparison with some existing ones. Finally, three numerical examples with simulation results are given to illustrate the correctness of the proposed results.

scholarly journals Stability Analysis for Memristor-Based Complex-Valued Neural Networks with Time Delays

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 120
Author(s):  
Ping Hou ◽  
Jun Hu ◽  
Jie Gao ◽  
Peican Zhu
Keyword(s):  
Numerical Simulation ◽  
Neural Networks ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Activation Functions ◽  
Complex Valued ◽  
Theoretical Results

In this paper, the problem of stability analysis for memristor-based complex-valued neural networks (MCVNNs) with time-varying delays is investigated extensively. This paper focuses on the exponential stability of the MCVNNs with time-varying delays. By means of the Brouwer’s fixed-point theorem and M-matrix, the existence, uniqueness, and exponential stability of the equilibrium point for MCVNNs are studied, and several sufficient conditions are obtained. In particular, these results can be applied to general MCVNNs whether the activation functions could be explicitly described by dividing into two parts of the real parts and imaginary parts or not. Two numerical simulation examples are provided to illustrate the effectiveness of the theoretical results.

Sign in / Sign up

Export Citation Format

Share Document