scholarly journals Globally asymptotical stability and periodicity for a nonautonomous two-species system with diffusion and impulses

2012 ◽  
Vol 36 (1) ◽  
pp. 288-300 ◽  
Author(s):  
Yuanfu Shao
Keyword(s):  
Asymptotical Stability ◽  
Globally Asymptotical Stability

PERMANENCE AND GLOBAL STABILITY IN AN IMPULSIVE LOTKA–VOLTERRA N-SPECIES COMPETITIVE SYSTEM WITH BOTH DISCRETE DELAYS AND CONTINUOUS DELAYS

2008 ◽  
Vol 01 (02) ◽  
pp. 179-196 ◽  
Author(s):  
XINZHU MENG ◽  
LANSUN CHEN
Keyword(s):  
Global Stability ◽  
Time Delays ◽  
Asymptotical Stability ◽  
Volterra System ◽  
Competitive System ◽  
Globally Asymptotical Stability ◽  
Discrete Delays ◽  
Impulsive Delay ◽  
Impulsive Perturbations

In this paper, we formulate a robust impulsive Lotka–Volterra n-species competitive system with both discrete delays and continuous delays. Our results in this paper indicate that under the appropriate linear bounded impulsive perturbations, the impulsive delay Lotka–Volterra system remains the original permanence and globally asymptotical stability of the nonimpulsive delay Lotka–Volterra system. We show that the conditions for the permanence and globally asymptotical stability of the system depend on time delays, so, we call it "profitless".

scholarly journals Stability of delay neural networks with uncertainties via delayed intermittent control

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yujuan Tian ◽  
Fei Wang ◽  
Yao Wang ◽  
Xiaodi Li
Keyword(s):  
Neural Networks ◽  
Functional Method ◽  
Asymptotical Stability ◽  
Linear Matrix ◽  
Intermittent Control ◽  
Weighting Matrix ◽  
Control Scheme ◽  
Globally Asymptotical Stability ◽  
The Stability ◽  
Delay Dependent

Abstract In this paper, we investigate the stability of neural networks with both time-varying delays and uncertainties. A novel delayed intermittent control scheme is designed to ensure the globally asymptotical stability of the addressed system. Some new delay dependent sufficient criteria for globally asymptotical stability results are derived in term of linear matrix inequalities (LMIs) by using free-weighting matrix techniques and Lyapunov–Krasovskii functional method. Finally, a numerical simulation is provided to show the effectiveness of the proposed approach.

Asymptotic stability of fractional difference equations with bounded time delays

2020 ◽  
Vol 23 (2) ◽  
pp. 571-590
Author(s):  
Mei Wang ◽  
Baoguo Jia ◽  
Feifei Du ◽  
Xiang Liu
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Difference Equations ◽  
Integral Inequality ◽  
Time Delays ◽  
Asymptotical Stability ◽  
Stability Conditions ◽  
Fractional Difference ◽  
Fractional Difference Equations ◽  
Fractional Difference Equation

AbstractIn this paper, an integral inequality and the fractional Halanay inequalities with bounded time delays in fractional difference are investigated. By these inequalities, the asymptotical stability conditions of Caputo and Riemann-Liouville fractional difference equation with bounded time delays are obtained. Several examples are presented to illustrate the results.

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