A graph-theoretic approach to exponential stability of BAM neural networks with delays and reaction-diffusion

2014 ◽  
Vol 94 (10) ◽  
pp. 2037-2056 ◽  
Author(s):  
Huan Su ◽  
Zhifang He ◽  
Yuwei Zhao ◽  
Xiaohua Ding
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Reaction Diffusion ◽  
Theoretic Approach ◽  
Bam Neural Networks ◽  
Graph Theoretic ◽  
Graph Theoretic Approach

scholarly journals Novel Lagrange sense exponential stability criteria for time-delayed stochastic Cohen–Grossberg neural networks with Markovian jump parameters: A graph-theoretic approach

2020 ◽  
Vol 25 (5) ◽  
Author(s):  
Iswarya Manickam ◽  
Raja Ramachandran ◽  
Grienggrai Rajchakit ◽  
Jinde Cao ◽  
Chuangxia Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Theoretic Approach ◽  
Markovian Jump ◽  
Markovian Jumping ◽  
Markovian Jump Parameters ◽  
Graph Theoretic ◽  
Mixed Time Delays ◽  
Graph Theoretic Approach

This paper concerns the issues of exponential stability in Lagrange sense for a class of stochastic Cohen–Grossberg neural networks (SCGNNs) with Markovian jump and mixed time delay effects. A systematic approach of constructing a global Lyapunov function for SCGNNs with mixed time delays and Markovian jumping is provided by applying the association of Lyapunov method and graph theory results. Moreover, by using some inequality techniques in Lyapunov-type and coefficient-type theorems we attain two kinds of sufficient conditions to ensure the global exponential stability (GES) through Lagrange sense for the addressed SCGNNs. Ultimately, some examples with numerical simulations are given to demonstrate the effectiveness of the acquired result.

scholarly journals Preserving Global Exponential Stability of Hybrid BAM Neural Networks with Reaction Diffusion Terms in the Presence of Stochastic Noise and Connection Weight Matrices Uncertainty

2014 ◽  
Vol 2014 ◽  
pp. 1-17
Author(s):  
Yan Li ◽  
Yi Shen
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Reaction Diffusion ◽  
Stochastic Noise ◽  
Bam Neural Networks ◽  
Connection Weight ◽  
Exponentially Stable ◽  
The Neural Networks ◽  
The Impact

We study the impact of stochastic noise and connection weight matrices uncertainty on global exponential stability of hybrid BAM neural networks with reaction diffusion terms. Given globally exponentially stable hybrid BAM neural networks with reaction diffusion terms, the question to be addressed here is how much stochastic noise and connection weights matrices uncertainty the neural networks can tolerate while maintaining global exponential stability. The upper threshold of stochastic noise and connection weights matrices uncertainty is defined by using the transcendental equations. We find that the perturbed hybrid BAM neural networks with reaction diffusion terms preserve global exponential stability if the intensity of both stochastic noise and connection weights matrices uncertainty is smaller than the defined upper threshold. A numerical example is also provided to illustrate the theoretical conclusion.

scholarly journals Dynamics of a Diffusive Multigroup SVIR Model with Nonlinear Incidence

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Jinhu Xu ◽  
Yan Geng
Keyword(s):  
Reproduction Number ◽  
Classical Method ◽  
Reaction Diffusion ◽  
Theoretic Approach ◽  
Globally Asymptotically Stable ◽  
Nonlinear Incidence ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Special Case ◽  
Disease Free

In this paper, a multigroup SVIR epidemic model with reaction-diffusion and nonlinear incidence is investigated. We first establish the well-posedness of the model. Then, the basic reproduction number ℜ 0 is established and shown as a threshold: the disease-free steady state is globally asymptotically stable if ℜ 0 < 1 , while the disease will be persistent when ℜ 0 > 1 . Moreover, applying the classical method of Lyapunov and a recently developed graph-theoretic approach, we established the global stability of the endemic equilibria for a special case.

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