scholarly journals On the Practical Stability of the Solutions of Impulsive Systems of Differential-Difference Equations with Variable Impulsive Perturbations

1996 ◽  
Vol 200 (2) ◽  
pp. 272-288 ◽  
Author(s):  
Drumi D. Bainov ◽  
Ivanka M. Stamova
Keyword(s):  
Difference Equations ◽  
Practical Stability ◽  
Impulsive Systems ◽  
Impulsive Perturbations

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 Existence of Center for Planar Differential Systems with Impulsive Perturbations

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Dengguo Xu
Keyword(s):  
Computing Methods ◽  
Impulsive Systems ◽  
Differential Systems ◽  
Numerical Examples ◽  
State Dependent ◽  
Planar Systems ◽  
Linear And Nonlinear ◽  
Impulsive Perturbations ◽  
The Stability ◽  
Theoretical Results

We present a method that uses successor functions in ordinary differential systems to address the “center-focus” problem of a class of planar systems that have an impulsive perturbation. By deriving solution formulae for impulsive systems, several interesting criteria for distinguishing between the center and the focus of linear and nonlinear planar systems with state-dependent impulsions are established. The conditions describing the stability of the focus of the considered models are also given. The computing methods presented here are more convenient for determining the center of impulsive systems than those in the literature. Numerical examples are given to show the effectiveness of the theoretical results.

scholarly journals Practical Stability with Respect to h-Manifolds for Impulsive Control Functional Differential Equations with Variable Impulsive Perturbations

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 656 ◽  
Author(s):  
Gani Stamov ◽  
Ivanka Stamova ◽  
Xiaodi Li ◽  
Ekaterina Gospodinova
Keyword(s):  
Differential Equations ◽  
Impulsive Control ◽  
Functional Differential Equations ◽  
Cellular Neural Network ◽  
Continuous Functions ◽  
Practical Stability ◽  
Piecewise Continuous ◽  
Impulsive Perturbations ◽  
Functional Differential ◽  
Control Functional

The present paper is devoted to the problems of practical stability with respect to h-manifolds for impulsive control differential equations with variable impulsive perturbations. We will consider these problems in light of the Lyapunov–Razumikhin method of piecewise continuous functions. The new results are applied to an impulsive control cellular neural network model with variable impulsive perturbations.

scholarly journals A Note on Practical Stability of Nonlinear Vibration Systems with Impulsive Effects

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Qishui Zhong ◽  
Hongcai Li ◽  
Hui Liu ◽  
Juebang Yu
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Nonlinear Vibration ◽  
Stability Criterion ◽  
Fuzzy Model ◽  
Vibration Characteristics ◽  
Impulsive Effects ◽  
Practical Stability ◽  
Impulsive Systems ◽  
System A

This paper addresses the issue of vibration characteristics of nonlinear systems with impulsive effects. By utilizing a T-S fuzzy model to represent a nonlinear system, a general strict practical stability criterion is derived for nonlinear impulsive systems.

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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