scholarly journals Orbital stability of periodic solutions of an impulsive system with a linear continuous-time part

2020 ◽  
Vol 5 (1) ◽  
pp. 96-110 ◽  
Author(s):  
Alexander N. Churilov ◽  
Keyword(s):  
Periodic Solutions ◽  
Continuous Time ◽  
Orbital Stability ◽  
Impulsive System ◽  
Time Part

scholarly journals Positive Periodic Solutions of Cooperative Systems with Delays and Feedback Controls

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Tursuneli Niyaz ◽  
Ahmadjan Muhammadhaji
Keyword(s):  
Periodic Solutions ◽  
Continuous Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Positive Periodic Solutions ◽  
Feedback Controls ◽  
Volterra Systems

This paper studies a class of periodicnspecies cooperative Lotka-Volterra systems with continuous time delays and feedback controls. Based on the continuation theorem of the coincidence degree theory developed by Gaines and Mawhin, some new sufficient conditions on the existence of positive periodic solutions are established.

PERIODIC SOLUTIONS OF TWO-SPECIES DIFFUSION MODELS WITH CONTINUOUS TIME DELAYS*

2002 ◽  
Vol 35 (2) ◽  
pp. 433-448 ◽  
Author(s):  
Hai-Feng Huo ◽  
Wan-Tong Li ◽  
Sui Sun Cheng
Keyword(s):  
Periodic Solutions ◽  
Continuous Time ◽  
Time Delays ◽  
Diffusion Models ◽  
Species Diffusion

scholarly journals Positive Periodic Solutions of a Neutral Impulsive Predator-Prey Model

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Guirong Liu ◽  
Xiaojuan Song
Keyword(s):  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Impulsive System ◽  
Impulsive Effect ◽  
Neutral System ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

We investigate a ratio-dependent predator-prey model with Holling type III functional response based on system of neutral impulsive differential equations. Sufficient conditions for existence of positive periodic solutions are obtained by applying continuation theorem. Our main results demonstrate that under the suitable periodic impulse perturbations, the neutral impulsive system preserves the periodicity of the corresponding neutral system without impulse. In addition, our results can be applied to the corresponding system without impulsive effect, and thus, extend previous results.

FORCED DIFFUSION EQUATION WITH PIECEWISE CONTINUOUS TIME DELAY

2021 ◽  
Vol 10 (4) ◽  
pp. 2269-2283
Author(s):  
M. Muminov ◽  
T. Radjabov
Keyword(s):  
Time Delay ◽  
Diffusion Equation ◽  
Periodic Solutions ◽  
Continuous Time ◽  
Algebraic Equations ◽  
Piecewise Constant Arguments ◽  
Piecewise Constant ◽  
Continuous Time Delay ◽  
Piecewise Continuous ◽  
Forced Diffusion

In this article, we study the boundary value problem (BVP) for forced diffusion equation with piecewise constant arguments. We give explicit formula for solving BVP. The problem of finding periodic solutions of some differential equations with piecewise constant arguments (DEPCA) is reduced to solving a system of algebraic equations. Using the method of finding periodic solutions of DEPCA, the solutions of BVP are given in several examples which are periodic in time.

A MONOTONE-ITERATIVE METHOD FOR FINDING PERIODIC SOLUTION OF AN IMPULSIVE DIFFERENTIAL EQUATIONS AND APPLICATION

2008 ◽  
Vol 01 (02) ◽  
pp. 247-256
Author(s):  
JIAWEI DOU
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Upper And Lower Solutions ◽  
Impulsive Differential Equations ◽  
Iteration Process ◽  
Impulsive System ◽  
Monotone Iterative Method ◽  
Initial Value ◽  
Monotone Iterative ◽  
Monotone Iterations

In this paper, using the method of upper and lower solutions and its associated monotone iterations, we establish a new monotone-iterative scheme for finding periodic solutions of an impulsive differential equations. This method leads to the existence of maximal and minimal periodic solutions which can be computed from a linear iteration process in the same fashion as for impulsive differential equations initial value problem. This method is constructive and can be used to develop a computational algorithm for numerical solution of the periodic impulsive system. Our existence result improves a result established in [1]. The result is applied to a model of mutualism of Lotka–Volterra type which involves interactions among a mutualist-competitor, a competitor and a mutualist, the existence of positive periodic solutions of the model is obtained.

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