scholarly journals New Asymptotical Stability and Uniformly Asymptotical Stability Theorems for Nonautonomous Difference Equations

2016 ◽  
Vol 07 (10) ◽  
pp. 1023-1031
Author(s):  
Limin Zhang ◽  
Chaofeng Zhang
Keyword(s):  
Difference Equations ◽  
Asymptotical Stability ◽  
Stability Theorems ◽  
Uniformly Asymptotical Stability

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.

Three Asymptotical Stability Theorems on Partial Region with Applications

1998 ◽  
Vol 37 (Part 1, No. 5A) ◽  
pp. 2762-2773 ◽  
Author(s):  
Zheng-Ming Ge ◽  
Jung-Kui Yu ◽  
Hsien-Keng Chen
Keyword(s):  
Asymptotical Stability ◽  
Partial Region ◽  
Stability Theorems

PERMANENCE AND UNIFORMLY ASYMPTOTICAL STABILITY OF ALMOST PERIODIC SOLUTIONS FOR A SINGLE-SPECIES MODEL WITH FEEDBACK CONTROL ON TIME SCALES

2014 ◽  
Vol 07 (01) ◽  
pp. 1450004 ◽  
Author(s):  
Yongkun Li ◽  
Li Yang ◽  
Hongtao Zhang
Keyword(s):  
Feedback Control ◽  
Periodic Solutions ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Single Species ◽  
Asymptotical Stability ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Uniformly Asymptotical Stability ◽  
Single Species Model

In this paper, using the time scale calculus theory, we first discuss the permanence of a single-species model with feedback control on time scales. Based on the permanence result, by the Lyapunov functional method, we establish sufficient conditions for the existence and uniformly asymptotical stability of almost periodic solutions of the considered model. Moreover, we present an illustrative example to show the effectiveness of obtained results.

scholarly journals Second method of Lyapunov for stability of linear impulsive differential-difference equations with variable impulsive perturbations

1998 ◽  
Vol 11 (2) ◽  
pp. 209-216 ◽  
Author(s):  
D. D. Bainov ◽  
I. M. Stamova ◽  
A. S. Vatsala
Keyword(s):  
Difference Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Asymptotical Stability ◽  
Uniform Stability ◽  
Auxiliary Functions ◽  
Piecewise Continuous ◽  
Impulsive Perturbations ◽  
Second Method Of Lyapunov

The present work is devoted to the study of stability of the zero solution to linear impulsive differential-difference equations with variable impulsive perturbations. With the aid of piecewise continuous auxiliary functions, which are generalizations of the classical Lyapunov's functions, sufficient conditions are found for the uniform stability and uniform asymptotical stability of the zero solution to equations under consideration.

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