scholarly journals Note on the Persistence of a Nonautonomous Lotka-Volterra Competitive System with Infinite Delay and Feedback Controls

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Chunling Shi ◽  
Yiqin Wang ◽  
Xiaoying Chen ◽  
Yuli Chen
Keyword(s):  
Numerical Simulations ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Competitive System ◽  
Feedback Controls ◽  
Special Case

We study a nonautonomous Lotka-Volterra competitive system with infinite delay and feedback controls. We establish a series of criteria under which a part ofn-species of the systems is driven to extinction while the remaining part of the species is persistent. Particularly, as a special case, a series of new sufficient conditions on the persistence for all species of system are obtained. Several examples together with their numerical simulations show the feasibility of our main results.

Extinction in a discrete Lotka–Volterra competitive system with the effect of toxic substances and feedback controls

2015 ◽  
Vol 08 (01) ◽  
pp. 1550012 ◽  
Author(s):  
Lijuan Chen ◽  
Fengde Chen
Keyword(s):  
Feedback Control ◽  
Lyapunov Function ◽  
Numerical Simulations ◽  
Sufficient Conditions ◽  
The Other ◽  
Toxic Substances ◽  
Two Dimensional ◽  
Competitive System ◽  
Feedback Controls ◽  
Analysis Technique

In this paper, we consider a discrete Lotka–Volterra competitive system with the effect of toxic substances and feedback controls. By using the method of discrete Lyapunov function and by developing a new analysis technique, we obtain the sufficient conditions which guarantee that one of the two species will be driven to extinction while the other will be permanent. We improve the corresponding results of Li and Chen [Extinction in two-dimensional discrete Lotka–Volterra competitive system with the effect of toxic substances, Dynam. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 15 (2008) 165–178]. Also, an example together with their numerical simulations shows the feasibility of our main results. It is shown that toxic substances and feedback control variables play an important role in the dynamics of the system.

scholarly journals Almost periodic solution of a discrete competitive system with delays and feedback controls

2019 ◽  
Vol 17 (1) ◽  
pp. 120-130 ◽  
Author(s):  
Yalong Xue ◽  
Xiangdong Xie ◽  
Qifa Lin
Keyword(s):  
Numerical Simulation ◽  
Periodic Solution ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Competitive System ◽  
Feedback Controls ◽  
Uniformly Asymptotic Stability ◽  
Positive Almost Periodic Solution

Abstract A discrete nonlinear almost periodic multispecies competitive system with delays and feedback controls is proposed and investigated. We obtain sufficient conditions to ensure the permanence of the system. Also, we establish a criterion for the existence and uniformly asymptotic stability of unique positive almost periodic solution of the system. In additional, an example together with its numerical simulation are presented to illustrate the feasibility of the main result.

scholarly journals Extinction in Two-Species Nonlinear Discrete Competitive System

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Liqiong Pu ◽  
Xiangdong Xie ◽  
Fengde Chen ◽  
Zhanshuai Miao
Keyword(s):  
Numerical Simulations ◽  
Positive Solution ◽  
Discrete System ◽  
Sufficient Conditions ◽  
The Other ◽  
Discrete Equation ◽  
Toxic Substances ◽  
Competitive System ◽  
Globally Attractive ◽  
Nonlinear Discrete System

We propose a nonlinear discrete system of two species with the effect of toxic substances. By constructing a suitable Lyapunov-type function, we obtain the sufficient conditions which guarantee that one of the components will be driven to extinction while the other will be globally attractive with any positive solution of a discrete equation. Two examples together with their numerical simulations illustrate the feasibility of our main results. The results not only improve but also complement some known results.

scholarly journals Dynamic Behaviors of a Competitive System with Beddington-DeAngelis Functional Response

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Shengbin Yu ◽  
Fengde Chen
Keyword(s):  
Periodic Solution ◽  
Numerical Simulations ◽  
Functional Response ◽  
Recent Literature ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Competitive System ◽  
Dynamic Behaviors ◽  
Partial Extinction

This article studies a competitive system with Beddington-DeAngelis functional response and establishes sufficient conditions on permanence, partial extinction, and the existence of a unique almost periodic solution for the system. The results supplement and generalize the main conclusions in recent literature. Numerical simulations have been presented to validate the analytical results.

Dynamics of delayed stochastic predator–prey models with feedback controls based on discrete observations

2017 ◽  
Vol 10 (03) ◽  
pp. 1750040 ◽  
Author(s):  
Dianli Zhao ◽  
Sanling Yuan
Keyword(s):  
Numerical Simulations ◽  
Stochastic System ◽  
Necessary Conditions ◽  
Deterministic Model ◽  
Sufficient Conditions ◽  
Discrete Observations ◽  
Feedback Controls ◽  
Predator Prey ◽  
Global Positive Solution ◽  
Predator Prey Models

In this paper, we concern a class of the generalized delayed stochastic predator–prey models with feedback controls based on discrete observations. The existence of global positive solution is given first. Then we discuss the deterministic model briefly, and establish the necessary conditions and the sufficient conditions for almost-sure extinction and persistence in mean for the stochastic system, where we show that the feedback controls can change the properties of the population systems significantly. Finally, numerical simulations are introduced to support the main results.

scholarly journals Extinction in Nonautonomous Discrete Lotka-Volterra Competitive System with Pure Delays and Feedback Controls

2009 ◽  
Vol 2009 ◽  
pp. 1-19 ◽  
Author(s):  
Ling Zhang ◽  
Zhidong Teng ◽  
Tailei Zhang ◽  
Shujing Gao
Keyword(s):  
Discrete Time ◽  
Sufficient Conditions ◽  
Lyapunov Functionals ◽  
Competitive System ◽  
Feedback Controls

The paper discusses a nonautonomous discrete time Lotka-Volterra competitive system with pure delays and feedback controls. New sufficient conditions for which a part of then-species is driven to extinction are established by using the method of multiple discrete Lyapunov functionals.

scholarly journals Asymptotic Behavior of Positive Solutions of a Competitive System Subject to Environmental Noise

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Huili Xiang ◽  
Zhuang Fang ◽  
Zuxiong Li ◽  
Zhijun Liu
Keyword(s):  
Asymptotic Behavior ◽  
Lyapunov Function ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Stochastic Differential Equations ◽  
Positive Solution ◽  
Sufficient Conditions ◽  
Environmental Noise ◽  
Competitive System ◽  
Stochastic Boundedness

A competitive system subject to environmental noise is established. By using the theory of stochastic differential equations and Lyapunov function, sufficient conditions for the existence, uniqueness, stochastic boundedness, and global attraction of the positive solution of the above system are established, respectively. An example together with its corresponding numerical simulations is presented to confirm our analytical results.

GLOBAL SOLUTIONS AND BOUNDEDNESS OF STOCHASTIC FUNCTIONAL KOLMOGOROV SYSTEM WITH INFINITE DELAY

2009 ◽  
Vol 09 (02) ◽  
pp. 315-333
Author(s):  
YONG XU ◽  
FUKE WU ◽  
SHIGENG HU
Keyword(s):  
Positive Solutions ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Global Solutions ◽  
Volterra Model ◽  
Kolmogorov System ◽  
Special Case ◽  
Stochastic Functional

This paper investigates the existence and boundedness of the global positive solutions for stochastic Kolmogorov system with infinite delay. We obtain two classes of sufficient conditions to guarantee these properties. These two classes of the conditions show that the system is dominated by deterministic part or stochastic part respectively. By the M-matrix technique, we conveniently compare our results. Finally, a Lotka–Volterra model as a special case is given to illustrate our idea.

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