Impulsive effects on global stability of models based on impulsive differential equations with “supremum” and variable impulsive perturbations

2013 ◽  
Vol 35 (1) ◽  
pp. 85-96 ◽  
Author(s):  
I. M. Stamova ◽  
T. G. Stamov
Keyword(s):  
Differential Equations ◽  
Global Stability ◽  
Impulsive Differential Equations ◽  
Impulsive Effects ◽  
Impulsive Perturbations

APPROXIMATE CONTROLLABILITY OF SECOND-ORDER STOCHASTIC DIFFERENTIAL EQUATIONS WITH IMPULSIVE EFFECTS

2010 ◽  
Vol 24 (14) ◽  
pp. 1559-1572 ◽  
Author(s):  
RATHINASAMY SAKTHIVEL ◽  
YONG REN ◽  
N. I. MAHMUDOV
Keyword(s):  
Biological Sciences ◽  
Differential Equations ◽  
Approximate Controllability ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Impulsive Effects ◽  
Infinite Dimensional ◽  
Infinite Dimensional Dynamical Systems ◽  
Necessary And Sufficient

Many practical systems in physical and biological sciences have impulsive dynamical behaviors during the evolution process which can be modeled by impulsive differential equations. In this paper, the approximate controllability of nonlinear second-order stochastic infinite-dimensional dynamical systems with impulsive effects is considered. By using the Holder's inequality, stochastic analysis and fixed point strategy, a new set of necessary and sufficient conditions are formulated which guarantees the approximate controllability of the nonlinear second-order stochastic system. The results are obtained under the assumption that the associated linear system is approximately controllable.

scholarly journals Oscillation of Second-Order Sublinear Impulsive Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
A. Zafer
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Oscillation Criteria ◽  
Impulsive Perturbations

Oscillation criteria obtained by Kusano and Onose (1973) and by Belohorec (1969) are extended to second-order sublinear impulsive differential equations of Emden-Fowler type:x″(t)+p(t)|x(τ(t))|α-1x(τ(t))=0,t≠θk;Δx'(t)|t=θk+qk|x(τ(θk))|α-1x(τ(θk))=0;Δx(t)|t=θk=0,  (0<α<1)by considering the casesτ(t)≤tandτ(t)=t, respectively. Examples are inserted to show how impulsive perturbations greatly affect the oscillation behavior of the solutions.

scholarly journals APPLICATIONS OF VARIATIONAL METHODS TO BOUNDARY-VALUE PROBLEM FOR IMPULSIVE DIFFERENTIAL EQUATIONS

2008 ◽  
Vol 51 (2) ◽  
pp. 509-527 ◽  
Author(s):  
Yu Tian ◽  
Weigao Ge
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Variational Methods ◽  
Positive Solutions ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Impulsive Effects ◽  
Differential Inequalities ◽  
Existence Of Positive Solutions ◽  
Sturm Liouville

AbstractIn this paper, we investigate the existence of positive solutions to a second-order Sturm–Liouville boundary-value problem with impulsive effects. The ideas involve differential inequalities and variational methods.

Analysis and control of a non-smooth population model with impulsive effects

2018 ◽  
Vol 11 (05) ◽  
pp. 1850074 ◽  
Author(s):  
Jing Na Liu ◽  
Tie Zhang ◽  
Lichun Zhao ◽  
Bing Liu
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Population Model ◽  
Global Analysis ◽  
Impulsive Differential Equations ◽  
Qualitative Theory ◽  
Impulsive Effects ◽  
Existence Conditions ◽  
And Control ◽  
Order One Periodic Solution

In this paper, a non-smooth population model with impulsive effects is proposed by combining discontinuity and non-smoothness. According to the qualitative theory of differential equations, the global analysis of the model is discussed. Using the theory of impulsive differential equations, the existence conditions of order one periodic solution are obtained. And the impulsive controllers are designed to make the pest populations stay at the refuge level. Some simulations are carried out to prove the results.

scholarly journals Dynamics of an Almost Periodic Food Chain System with Impulsive Effects

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Yaqin Li ◽  
Wenquan Wu ◽  
Tianwei Zhang
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Food Chain ◽  
Impulsive Differential Equations ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Chain System ◽  
Positive Almost Periodic Solution ◽  
Impulsive Perturbations

In order to obtain a more accurate description of the ecological system perturbed by human exploitation activities such as planting and harvesting, we need to consider the impulsive differential equations. Therefore, by applying the comparison theorem and the Lyapunov method of the impulsive differential equations, this paper gives some new sufficient conditions for the permanence and existence of a unique uniformly asymptotically stable positive almost periodic solution in a food chain system with almost periodic impulsive perturbations. The method used in this paper provides a possible method to study the permanence and existence of a unique uniformly asymptotically stable positive almost periodic solution of the models with impulsive perturbations in biological populations. Finally, an example and numerical simulations are given to illustrate that our results are feasible.

scholarly journals Stability and attractivity of solutions of differential equations with impulses at fixed times

2000 ◽  
Vol 13 (1) ◽  
pp. 77-84 ◽  
Author(s):  
S. Sivasundaram ◽  
S. Vassilyev
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Dynamic Properties ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Fixed Time ◽  
Impulsive Effects ◽  
Comparison Methods ◽  
Vector Lyapunov Functions ◽  
Fixed Times

In this paper we consider the dynamics of solutions of impulsive differential equations with fixed time moments of impulsive effects on the basis of comparison methods and vector Lyapunov functions. We propose sufficient conditions on the following dynamic properties: stability, attractivity, and some combinations of them.

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