scholarly journals Polyhedral Lyapunov functions structurally ensure global asymptotic stability of dynamical networks iff the Jacobian is non-singular

Automatica ◽  
2017 ◽  
Vol 86 ◽  
pp. 183-191 ◽  
Author(s):  
Franco Blanchini ◽  
Giulia Giordano
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Lyapunov Functions ◽  
Dynamical Networks

scholarly journals Global Asymptotic Stability of Stochastic Nonautonomous Lotka-Volterra Models with Infinite Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Fengying Wei ◽  
Yuhua Cai
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Stochastic Differential Equation ◽  
Global Asymptotic Stability ◽  
Existence And Uniqueness ◽  
Lyapunov Functions ◽  
Infinite Delay ◽  
Volterra Models ◽  
Global Positive Solution ◽  
Time Average

A kind of general stochastic nonautonomous Lotka-Volterra models with infinite delay is investigated in this paper. By constructing several suitable Lyapunov functions, the existence and uniqueness of global positive solution and global asymptotic stability are obtained. Further, the solution asymptotically follows a normal distribution by means of linearizing stochastic differential equation. Moment estimations in time average are derived to improve the approximation distribution. Finally, numerical simulations are given to illustrate our conclusions.

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.

Conditions for the local and global asymptotic stability of the time–fractional Degn–Harrison system

2020 ◽  
Vol 21 (7-8) ◽  
pp. 749-759
Author(s):  
Rachida Mezhoud ◽  
Khaled Saoudi ◽  
Abderrahmane Zaraï ◽  
Salem Abdelmalek
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linearization Method ◽  
Direct Lyapunov Method ◽  
Fractional Systems ◽  
Reaction Diffusion Model ◽  
Theoretical Results

AbstractFractional calculus has been shown to improve the dynamics of differential system models and provide a better understanding of their dynamics. This paper considers the time–fractional version of the Degn–Harrison reaction–diffusion model. Sufficient conditions are established for the local and global asymptotic stability of the model by means of invariant rectangles, the fundamental stability theory of fractional systems, the linearization method, and the direct Lyapunov method. Numerical simulation results are used to illustrate the theoretical results.

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