scholarly journals Second method of Lyapunov and comparison principle for impulsive differential–difference equations

1997 ◽  
Vol 38 (4) ◽  
pp. 489-505 ◽  
Author(s):  
D. D. Bainov ◽  
I. M. Stamova
Keyword(s):  
Comparison Principle ◽  
Difference Equations ◽  
Continuous Functions ◽  
Differential Inequalities ◽  
Impulse Effect ◽  
Comparison Equation ◽  
Piecewise Continuous ◽  
Second Method Of Lyapunov

AbstractIn the present paper questions related to stability and boundedness with respect to manifolds of solutions of impulsive differential-difference equations are considered. The investigations are carried out by means of piecewise-continuous functions which are analogues of the classical Lyapunov's functions. By means of a vectorial comparison equation and differential inequalities for piecewise-continuous functions, theorems are proved on stability and boundedness with respect to manifolds of solutions of impulsive differential-difference equations with impulse effect at fixed moments.

scholarly journals Practical stability of the solutions of impulsive systems of differential-difference equations via the method of comparison and some applications to population dynamics

2002 ◽  
Vol 43 (4) ◽  
pp. 525-539 ◽  
Author(s):  
D. D. Bainov ◽  
A. B. Dishliev ◽  
I. M. Stamova
Keyword(s):  
Population Dynamics ◽  
Difference Equations ◽  
Initial Value Problem ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Practical Stability ◽  
Differential Inequalities ◽  
Impulsive Systems ◽  
Initial Value ◽  
Piecewise Continuous

AbstractIn this paper we consider an initial value problem for systems of impulsive differential-difference equations is considered. Making use of the method of comparison and differential inequalities for piecewise continuous functions, sufficient conditions for practical stability of the solutions of such systems are obtained. Applications to population dynamics are also given.

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.

Almost Periodicity and Lyapunov's Functions for Impulsive Functional Differential Equations with Infinite Delays

2010 ◽  
Vol 53 (2) ◽  
pp. 367-377 ◽  
Author(s):  
Gani Tr. Stamov
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
Continuous Functions ◽  
Differential Inequalities ◽  
Almost Periodic ◽  
Infinite Delays ◽  
Piecewise Continuous ◽  
Functional Differential

AbstractThis paper studies the existence and uniqueness of almost periodic solutions of nonlinear impulsive functional differential equations with infinite delay. The results obtained are based on the Lyapunov–Razumikhin method and on differential inequalities for piecewise continuous functions.

scholarly journals A Class of Vector Lyapunov Functions for Stability Analysis of Nonlinear Impulsive Differential Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Zhang Qunli
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Lyapunov Functions ◽  
Continuous Functions ◽  
Impulsive Effect ◽  
Differential Inequalities ◽  
Differential Systems ◽  
Impulsive Differential Systems ◽  
Vector Lyapunov Functions ◽  
Piecewise Continuous

A novel and effective approach to stability of the solutions of nonlinear systems with impulsive effect is considered. The investigations are carried out by means of a class of vector Lyapunov functions and differential inequalities for piecewise continuous functions. Simulation examples are given to illustrate the presented results.

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