Matrix Measure Approach for Stability and Synchronization of Complex-Valued Neural Networks with Deviating Argument

This paper concentrates on global exponential stability and synchronization for complex-valued neural networks (CVNNs) with deviating argument by matrix measure approach. The Lyapunov function is no longer required, and some sufficient conditions are firstly obtained to ascertain the addressed system to be exponentially stable under different activation functions. Moreover, after designing a suitable controller, the synchronization of two complex-valued coupled neural networks is realized, and the derived condition is easy to be confirmed. Finally, some numerical examples are given to demonstrate the superiority and feasibility of the presented theoretical analysis and results.

Download Full-text

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

Complexity ◽

10.1155/2017/3826729 ◽

2017 ◽

Vol 2017 ◽

pp. 1-12 ◽

Cited By ~ 5

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.

Download Full-text

GLOBAL EXPONENTIAL STABILITY AND PERIODIC OSCILLATIONS OF REACTION–DIFFUSION BAM NEURAL NETWORKS WITH PERIODIC COEFFICIENTS AND GENERAL DELAYS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127407017215 ◽

2007 ◽

Vol 17 (01) ◽

pp. 129-142 ◽

Cited By ~ 20

Author(s):

QINGHUA ZHOU ◽

JIANHUA SUN ◽

GUANRONG CHEN

Keyword(s):

Neural Networks ◽

Exponential Stability ◽

Global Exponential Stability ◽

Sufficient Conditions ◽

Reaction Diffusion ◽

Activation Functions ◽

Bidirectional Associative Memory ◽

Connection Weight ◽

Periodic Coefficients ◽

Delay Dependent

For a large class of reaction–diffusion bidirectional associative memory (RDBAM) neural networks with periodic coefficients and general delays, several new delay-dependent or delay-independent sufficient conditions ensuring the existence and global exponential stability of a unique periodic solution are given, by constructing suitable Lyapunov functionals and employing some analytic techniques such as Poincaré mapping. The presented conditions are easily verifiable and useful in the design and applications of RDBAM neural networks. Moreover, the employed analytic techniques do not require the symmetry of the bidirectional connection weight matrix, the boundedness, monotonicity and differentiability of activation functions of the network. In several ways, the results generalize and improve those established in the current literature.

Download Full-text

Global exponential stability of delayed complex-valued neural networks with discontinuous activation functions

Neurocomputing ◽

10.1016/j.neucom.2020.02.006 ◽

2020 ◽

Vol 416 ◽

pp. 1-11

Author(s):

Jin Hu ◽

Haidong Tan ◽

Chunna Zeng

Keyword(s):

Neural Networks ◽

Exponential Stability ◽

Global Exponential Stability ◽

Activation Functions ◽

Discontinuous Activation ◽

Discontinuous Activation Functions ◽

Complex Valued

Download Full-text

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

Entropy ◽

10.3390/e21020120 ◽

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.

Download Full-text

MULTILAYER PERCEPTRONS TO APPROXIMATE COMPLEX VALUED FUNCTIONS

International Journal of Neural Systems ◽

10.1142/s0129065795000299 ◽

1995 ◽

Vol 06 (04) ◽

pp. 435-446 ◽

Cited By ~ 11

Author(s):

P. ARENA ◽

L. FORTUNA ◽

R. RE ◽

M.G. XIBILIA

Keyword(s):

Neural Networks ◽

Computational Complexity ◽

Feedforward Neural Networks ◽

Density Theorem ◽

Multilayer Perceptrons ◽

Activation Functions ◽

Approximation Properties ◽

Numerical Examples ◽

Continuous Complex ◽

Complex Valued

In this paper the approximation capabilities of different structures of complex feedforward neural networks, reported in the literature, have been theoretically analyzed. In particular a new density theorem for Complex Multilayer Perceptrons with complex valued non-analytic sigmoidal activation functions has been proven. Such a result makes Multilayer Perceptrons with complex valued neurons universal interpolators of continuous complex valued functions. Moreover the approximation properties of superpositions of analytic activation functions have been investigated, proving that such combinations are not dense in the set of continuous complex valued functions. Several numerical examples have also been reported in order to show the advantages introduced by Complex Multilayer Perceptrons in terms of computational complexity with respect to the classical real MLP.

Download Full-text

Global Exponential Stability of Periodic Solution for Neutral-Type Complex-Valued Neural Networks

Discrete Dynamics in Nature and Society ◽

10.1155/2016/1267954 ◽

2016 ◽

Vol 2016 ◽

pp. 1-10 ◽

Cited By ~ 4

Author(s):

Song Guo ◽

Bo Du

Keyword(s):

Neural Networks ◽

Exponential Stability ◽

Periodic Solutions ◽

Global Exponential Stability ◽

Neutral Type ◽

Sufficient Conditions ◽

Mawhin’S Continuation Theorem ◽

Type Complex ◽

Existence Of Periodic Solutions ◽

Complex Valued

This paper deals with a class of neutral-type complex-valued neural networks with delays. By means of Mawhin’s continuation theorem, some criteria on existence of periodic solutions are established for the neutral-type complex-valued neural networks. By constructing an appropriate Lyapunov-Krasovskii functional, some sufficient conditions are derived for the global exponential stability of periodic solutions to the neutral-type complex-valued neural networks. Finally, numerical examples are given to show the effectiveness and merits of the present results.

Download Full-text

Matrix measure method for global exponential stability of complex-valued recurrent neural networks with time-varying delays

Neural Networks ◽

10.1016/j.neunet.2015.07.003 ◽

2015 ◽

Vol 70 ◽

pp. 81-89 ◽

Cited By ~ 76

Author(s):

Weiqiang Gong ◽

Jinling Liang ◽

Jinde Cao

Keyword(s):

Neural Networks ◽

Exponential Stability ◽

Recurrent Neural Networks ◽

Global Exponential Stability ◽

Time Varying ◽

Matrix Measure ◽

Complex Valued

Download Full-text

Analysis and Design of Associative Memories for Memristive Neural Networks with Deviating Argument

Mathematical Problems in Engineering ◽

10.1155/2017/1057909 ◽

2017 ◽

Vol 2017 ◽

pp. 1-16

Author(s):

Jin-E Zhang

Keyword(s):

Neural Networks ◽

Existence And Uniqueness ◽

Global Exponential Stability ◽

Invariant Manifolds ◽

Sufficient Conditions ◽

Associative Memories ◽

Memristive Neural Networks ◽

Deviating Argument ◽

Analysis And Design ◽

Uniqueness Of The Solution

We investigate associative memories for memristive neural networks with deviating argument. Firstly, the existence and uniqueness of the solution for memristive neural networks with deviating argument are discussed. Next, some sufficient conditions for this class of neural networks to possess invariant manifolds are obtained. In addition, a global exponential stability criterion is presented. Then, analysis and design of autoassociative memories and heteroassociative memories for memristive neural networks with deviating argument are formulated, respectively. Finally, several numerical examples are given to demonstrate the effectiveness of the obtained results.

Download Full-text