Stability of a Set of Impulsive Equations

2011 ◽  
pp. 257-270
Keyword(s):  
Impulsive Equations

Stability analysis of set trajectories for families of impulsive equations

2017 ◽  
Vol 98 (4) ◽  
pp. 828-842 ◽  
Author(s):  
A. A. Martynyuk ◽  
I. M. Stamova
Keyword(s):  
Stability Analysis ◽  
Impulsive Equations

scholarly journals Oscillation Criteria of Third-Order Nonlinear Impulsive Differential Equations with Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Xiuxiang Liu
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Third Order ◽  
Oscillation Criteria ◽  
Impulsive Equations ◽  
Equations With Delay

This paper deals with the oscillation of third-order nonlinear impulsive equations with delay. The results in this paper improve and extend some results for the equations without impulses. Some examples are given to illustrate the main results.

scholarly journals Complex Behavior in a Fish Algae Consumption Model with Impulsive Control Strategy

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Jin Yang ◽  
Min Zhao
Keyword(s):  
Control Strategy ◽  
Small Amplitude ◽  
Impulsive Control ◽  
Asymptotically Stable ◽  
Perturbation Techniques ◽  
Globally Asymptotically Stable ◽  
Impulsive Equations ◽  
Consumption Model ◽  
The Rich ◽  
Impulsive Control Strategy

This paper investigates a dynamic mathematical model of fish algae consumption with an impulsive control strategy analytically. It is proved that the system has a globally asymptotically stable algae-eradication periodic solution and is permanent by using the theory of impulsive equations and small-amplitude perturbation techniques. Numerical results for impulsive perturbations demonstrate the rich dynamic behavior of the system. Further, we have also compared biological control with chemical control. All these results may be useful in controlling eutrophication.

Conjugacies for impulsive equations

2011 ◽  
Vol 55 (1) ◽  
pp. 65-78
Author(s):  
Luis Barreira ◽  
Claudia Valls
Keyword(s):  
Differential Equations ◽  
Direct Proof ◽  
Impulsive Differential Equations ◽  
Nonlinear Perturbations ◽  
Nonlinear Case ◽  
Exponential Dichotomies ◽  
Impulsive Equations ◽  
Linear Perturbations ◽  
Linear And Nonlinear ◽  
Topological Conjugacies

AbstractFor impulsive differential equations, we construct topological conjugacies between linear and nonlinear perturbations of non-uniform exponential dichotomies. In the case of linear perturbations, the topological conjugacies are constructed in a more or less explicit manner. In the nonlinear case, we obtain an appropriate version of the Grobman–Hartman Theorem for impulsive equations, with a simple and direct proof that involves no discretization of the dynamics.

scholarly journals The Solvability and Optimal Controls for Some Fractional Impulsive Equations of Order1< α<2

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Xianghu Liu ◽  
Zhenhai Liu ◽  
Maojun Bin
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Schauder’S Fixed Point Theorem ◽  
Sufficient Condition ◽  
Optimal Controls ◽  
Schauder's Fixed Point Theorem ◽  
Gronwall’S Inequality ◽  
Impulsive Equations

We study the existence of solutions and optimal controls for some fractional impulsive equations of order1< α<2. By means of Gronwall’s inequality and Leray-Schauder’s fixed point theorem, the sufficient condition for the existence of solutions and optimal controls is presented. Finally, an example is given to illustrate our main results.

scholarly journals The Solvability and Optimal Controls for Some Fractional Impulsive Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xianghu Liu ◽  
Zhenhai Liu ◽  
Jiangfeng Han
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Calculus ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Sufficient Condition ◽  
Optimal Controls ◽  
Uniqueness Of Solutions ◽  
Impulsive Equations ◽  
Impulsive Equation

This paper is concerned with the existence and uniqueness of mild solution of some fractional impulsive equations. Firstly, we introduce the fractional calculus, Gronwall inequality, and Leray-Schauder’s fixed point theorem. Secondly with the help of them, the sufficient condition for the existence and uniqueness of solutions is presented. Finally we give an example to illustrate our main results.

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