scholarly journals Asymptotic stability of competitive systems with delays and impulsive perturbations

2007 ◽  
Vol 334 (1) ◽  
pp. 686-700 ◽  
Author(s):  
Shair Ahmad ◽  
Ivanka M. Stamova
Keyword(s):  
Asymptotic Stability ◽  
Competitive Systems ◽  
Impulsive Perturbations

Stability of impulsively perturbed systems

1977 ◽  
Vol 16 (1) ◽  
pp. 99-110 ◽  
Author(s):  
M. Rama Mohana Rao ◽  
V. Sree Hari Rao
Keyword(s):  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Perturbed Systems ◽  
Impulsive Perturbations

Until recently most authors have devoted their research to the theory of perturbed systems under continuous perturbations. In this paper, Liapunov's second method is employed to investigate sufficient conditions for integral and integral asymptotic stability of ordinary differential systems with respect to impulsive perturbations.

scholarly journals Permanence and Almost Periodic Solutions for N-Species Nonautonomous Lotka-Volterra Competitive Systems with Delays and Impulsive Perturbations on Time Scales

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Xuxu Yu ◽  
Qiru Wang ◽  
Yuzhen Bai
Keyword(s):  
Time Scales ◽  
Type Theorem ◽  
Sufficient Conditions ◽  
Comparison Theorems ◽  
Dynamic Equations ◽  
Almost Periodic ◽  
Competitive Systems ◽  
Uniformly Asymptotic Stability ◽  
Positive Almost Periodic Solution ◽  
Impulsive Perturbations

We investigate a class of nonautonomous N-species Lotka-Volterra-type competitive systems with time delays and impulsive perturbations on time scales. By using comparison theorems of impulsive dynamic equations on time scales, we obtain sufficient conditions to guarantee the permanence of the system. Then based on the Massera-type theorem for impulsive dynamic equations on time scales, we establish existence and uniformly asymptotic stability of the unique positive almost periodic solution of the system. Finally, an example is employed to illustrate our main results.

scholarly journals Asymptotic Stability of a Class of Impulsive Delay Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
G. L. Zhang ◽  
M. H. Song ◽  
M. Z. Liu
Keyword(s):  
Numerical Methods ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Analytic Solutions ◽  
Impulsive Delay Differential Equations ◽  
Impulsive Delay ◽  
Impulsive Perturbations ◽  
Delay Differential

This paper is concerned with a class of linear impulsive delay differential equations. Asymptotic stability of analytic solutions of this kind of equations is studied by the property of delay differential equations without impulsive perturbations. New numerical methods for this kind of equations are constructed. The convergence and asymptotic stability of the methods for this kind of equations are studied.

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