scholarly journals Global stability of delayed Hopfield neural networks under dynamical thresholds

2005 ◽  
Vol 2005 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Fei-Yu Zhang ◽  
Wan-Tong Li
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Topological Degree ◽  
Lyapunov Functions ◽  
Global Exponential Stability ◽  
Dynamical Behavior ◽  
Degree Theory ◽  
Topological Degree Theory ◽  
New Criteria

We study dynamical behavior of a class of cellular neural networks system with distributed delays under dynamical thresholds. By using topological degree theory and Lyapunov functions, some new criteria ensuring the existence, uniqueness, global asymptotic stability, and global exponential stability of equilibrium point are derived. In particular, our criteria generalize and improve some known results in the literature.

scholarly journals Global stability of Hopfield neural networks under dynamical thresholds with distributed delays

2006 ◽  
Vol 2006 ◽  
pp. 1-11
Author(s):  
Fei-Yu Zhang ◽  
Hai-Feng Huo
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Equilibrium Point ◽  
Global Asymptotic Stability ◽  
Dynamical Behavior ◽  
Hopfield Neural Networks ◽  
Distributed Delays ◽  
Connection Matrix ◽  
Activation Functions ◽  
New Criteria

We study the dynamical behavior of a class of Hopfield neural networks with distributed delays under dynamical thresholds. Some new criteria ensuring the existence, uniqueness, and global asymptotic stability of equilibrium point are derived. In the results, we do not require the activation functions to satisfy the Lipschitz condition, and also not to be bounded, differentiable, or monotone nondecreasing. Moreover, the symmetry of the connection matrix is not also necessary. Thus, our results improve some previous works in the literature. These conditions have great importance in designs and applications of the global asymptotic stability for Hopfield neural networks involving distributed delays under dynamical thresholds.

IMPULSIVE EFFECT OF CONTINUOUS-TIME NEURAL NETWORKS UNDER PURE STRUCTURAL VARIATIONS

2007 ◽  
Vol 17 (06) ◽  
pp. 2127-2139 ◽  
Author(s):  
ZHANJI GUI ◽  
WEIGAO GE
Keyword(s):  
Neural Networks ◽  
Continuous Time ◽  
Lyapunov Functions ◽  
Global Exponential Stability ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Simulation Method ◽  
Impulsive Effect ◽  
Structural Variations ◽  
Impulsive Perturbations

By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, we study the existence, uniqueness and global exponential stability of periodic solution for continuous-time neural networks under pure structural variations with impulsive perturbations: [Formula: see text] The results extend earlier ones where impulses are absent. Further, using numerical simulation method the influences of the impulsive perturbations on the inherent oscillation are investigated.

scholarly journals Dynamic behaviors for inertial neural networks with reaction-diffusion terms and distributed delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Famei Zheng
Keyword(s):  
Neural Networks ◽  
Equilibrium Point ◽  
Existence And Uniqueness ◽  
Global Exponential Stability ◽  
Degree Theory ◽  
Reaction Diffusion ◽  
Distributed Delays ◽  
Sufficient Condition ◽  
Topological Degree Theory ◽  
Inertial Neural Networks

AbstractA class of inertial neural networks (INNs) with reaction-diffusion terms and distributed delays is studied. The existence and uniqueness of the equilibrium point for the considered system is obtained by topological degree theory, and a sufficient condition is given to guarantee global exponential stability of the equilibrium point. Finally, an example is given to show the effectiveness of the results in this paper.

Dynamical behaviors of the generalized hematopoiesis model with discontinuous harvesting terms

2019 ◽  
Vol 12 (01) ◽  
pp. 1950009 ◽  
Author(s):  
Fanchao Kong
Keyword(s):  
Nonsmooth Analysis ◽  
Global Exponential Stability ◽  
Degree Theory ◽  
Topological Degree Theory ◽  
Filippov Solution ◽  
Dynamical Behaviors ◽  
Analysis Theory ◽  
Autonomous Case ◽  
Hematopoiesis Model ◽  
New Criteria

This paper is concerned with the generalized hematopoiesis model with discontinuous harvesting terms. Under the framework of Filippov solution, by means of the differential inclusions and the topological degree theory in set-valued analysis, we have established the existence of the bounded positive periodic solutions for the addressed models. After that, based on the nonsmooth analysis theory with Lyapunov-like approach, we employ a novel argument and derive some new criteria on the uniqueness, global exponential stability of the addressed models and convergence of the corresponding autonomous case of the addressed models. Our results extend previous works on hematopoiesis model to the discontinuous harvesting terms and some corresponding results in the literature can be enriched and extended. In addition, typical examples with numerical simulations are given to illustrate the feasibility and validity of obtained results.

New Asymptotic Stability and Uniqueness Results on Periodic Solutions of Second Order Differential Equations Using Degree Theory

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Manuel Zamora
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
Degree Theory ◽  
Second Order ◽  
Topological Degree Theory ◽  
Second Order Differential Equations ◽  
Uniqueness Results ◽  
New Criteria

AbstractWe present new criteria for uniqueness and asymptotic stability of periodic solutions of a second order differential equation based on topological degree theory. As an application, we will study some well known equations and some illustrative examples.

scholarly journals Global Asymptotic Stability of Switched Neural Networks with Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Zhenyu Lu ◽  
Kai Li ◽  
Yan Li
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Linear Matrix Inequalities ◽  
Global Asymptotic Stability ◽  
Recent Literature ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Numerical Example ◽  
Switched Neural Networks ◽  
New Criteria

This paper investigates the global asymptotic stability of a class of switched neural networks with delays. Several new criteria ensuring global asymptotic stability in terms of linear matrix inequalities (LMIs) are obtained via Lyapunov-Krasovskii functional. And here, we adopt the quadratic convex approach, which is different from the linear and reciprocal convex combinations that are extensively used in recent literature. In addition, the proposed results here are very easy to be verified and complemented. Finally, a numerical example is provided to illustrate the effectiveness of the results.

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