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.

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 Passivity analysis of multiple time-varying time delayed complex variable neural networks in finite-time

2021 ◽  
Vol 8 (4) ◽  
pp. 842-854
Author(s):  
N. Jayanthi ◽  
◽  
R. Santhakumari ◽  
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Multiple Time ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Complex Valued ◽  
Theoretical Results

In this article, we investigate the problem of finite-time passivity for the complex-valued neural networks (CVNNs) with multiple time-varying delays. To begin, many definitions relevant to the finite-time passivity of CVNNs are provided; then the suitable control inputs are designed to guarantee the class of CVNNs are finite-time passive. In the meantime, some sufficient conditions of linear matrix inequalities (LMIs) are derived by using inequalities techniques and Lyapunov stability theory. Finally, a numerical example is presented to illustrate the usefulness of the theoretical results.

Complex Neural Network Models for Time-Varying Drazin Inverse

2016 ◽  
Vol 28 (12) ◽  
pp. 2790-2824 ◽  
Author(s):  
Xue-Zhong Wang ◽  
Yimin Wei ◽  
Predrag S. Stanimirović
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Convergence Analysis ◽  
Network Models ◽  
Drazin Inverse ◽  
Time Varying ◽  
Activation Functions ◽  
Neural Network Models ◽  
Complex Valued ◽  
Theoretical Results

Two complex Zhang neural network (ZNN) models for computing the Drazin inverse of arbitrary time-varying complex square matrix are presented. The design of these neural networks is based on corresponding matrix-valued error functions arising from the limit representations of the Drazin inverse. Two types of activation functions, appropriate for handling complex matrices, are exploited to develop each of these networks. Theoretical results of convergence analysis are presented to show the desirable properties of the proposed complex-valued ZNN models. Numerical results further demonstrate the effectiveness of the proposed models.

PERIODICITY AND STABILITY IN RECURRENT CELLULAR NEURAL NETWORKS WITH IMPULSIVE EFFECTS

2011 ◽  
Vol 04 (04) ◽  
pp. 399-422 ◽  
Author(s):  
HAIBO GU ◽  
HAIJUN JIANG ◽  
ZHIDONG TENG
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Activation Functions ◽  
Analysis Problem ◽  
Mawhin’S Continuation Theorem

In this paper, the exponential stability analysis problem is considered for a class of impulsive recurrent cellular neural networks (IRCNNs) with time-varying delays. Without assuming the boundedness on the activation functions, some sufficient conditions are derived for checking the existence and exponential stability of periodic solution for this system by using Mawhin's continuation theorem of coincidence degree theory and constructing suitable Lyapunov functional. It is believed that these results are significant and useful for the design and applications of IRCNNs. Finally, an example with numerical simulation is given to show the effectiveness of the proposed method and results.

EXPONENTIAL STABILITY OF REACTION–DIFFUSION FUZZY RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

2007 ◽  
Vol 17 (09) ◽  
pp. 3099-3108 ◽  
Author(s):  
QINGHUA ZHOU ◽  
LI WAN ◽  
JIANHUA SUN
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Time Varying ◽  
Matrix Properties ◽  
Inequality Technique ◽  
Delay Dependent ◽  
Theoretical Results

Exponential stability of reaction–diffusion fuzzy recurrent neural networks (RDFRNNs) with time-varying delays are considered. By using the method of variational parameters, M-matrix properties and inequality technique, some delay-independent or delay-dependent sufficient conditions for guaranteeing the exponential stability of an equilibrium solution are obtained. One example is given to demonstrate the theoretical results.

scholarly journals Exponential Stability of Antiperiodic Solution for BAM Neural Networks with Time-Varying Delays

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaofei Li ◽  
Chuan Qin ◽  
Quanxin Zhu
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Exponential Stability ◽  
Negative Feedback ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Activation Functions ◽  
Leakage Delays ◽  
Inequality Techniques

In this paper, a kind of BAM neural networks with leakage delays in the negative feedback terms and time-varying delays in activation functions was considered. By constructing a suitable Lyapunov function and using inequality techniques, some sufficient conditions to ensure the existence and exponential stability of antiperiodic solutions of these neural networks were derived. These conditions extend some results recently appearing in recent papers. Lastly, an example is given to show the feasibility of these conditions.

scholarly journals Exponential Stability of BAM Fuzzy Cellular Neural Networks with Time-Varying Delays in Leakage Terms and Impulses

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yongkun Li ◽  
Youqin Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
Inequality Techniques ◽  
Theoretical Results

BAM fuzzy cellular neural networks with time-varying delays in leakage terms and impulses are considered. Some sufficient conditions for the exponential stability of the networks are established by using differential inequality techniques. The results of this paper are completely new and complementary to the previously known results. Finally, an example is given to demonstrate the effectiveness and conservativeness of our theoretical results.

Sign in / Sign up

Export Citation Format

Share Document