scholarly journals Global Attractivity and Extinction of a Discrete Competitive System with Infinite Delays and Single Feedback Control

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Yalong Xue ◽  
Xiangdong Xie ◽  
Qifa Lin ◽  
Fengde Chen
Keyword(s):  
Feedback Control ◽  
Comparison Theorem ◽  
Global Attractivity ◽  
Control Variable ◽  
Sufficient Conditions ◽  
Lyapunov Functionals ◽  
Species Competition ◽  
Competitive System ◽  
Competition System ◽  
Infinite Delays

A nonautonomous discrete two-species competition system with infinite delays and single feedback control is considered in this paper. Based on the discrete comparison theorem, a set of sufficient conditions which guarantee the permanence of the system is obtained. Then, by constructing some suitable discrete Lyapunov functionals, some sufficient conditions for the global attractivity and extinction of the system are obtained. It is shown that, by choosing some suitable feedback control variable, one of two species will be driven to extinction.

scholarly journals Dynamic Behaviors of a Discrete Lotka-Volterra Competition System with Infinite Delays and Single Feedback Control

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Liang Zhao ◽  
Xiangdong Xie ◽  
Liya Yang ◽  
Fengde Chen
Keyword(s):  
Biological Control ◽  
Feedback Control ◽  
Comparison Theorem ◽  
Global Attractivity ◽  
Control Variable ◽  
Sufficient Conditions ◽  
Lyapunov Functionals ◽  
Competitive System ◽  
Competition System ◽  
Infinite Delays

A nonautonomous discrete two-species Lotka-Volterra competition system with infinite delays and single feedback control is considered in this paper. By applying the discrete comparison theorem, a set of sufficient conditions which guarantee the permanence of the system is obtained. Also, by constructing some suitable discrete Lyapunov functionals, some sufficient conditions for the global attractivity and extinction of the system are obtained. It is shown that if the the discrete Lotka-Volterra competitive system with infinite delays and without feedback control is permanent, then, by choosing some suitable feedback control variable, the permanent species will be driven to extinction. That is, the feedback control variable, which represents the biological control or some harvesting procedure, is the unstable factor of the system. Such a finding overturns the previous scholars’ recognition on feedback control variables.

scholarly journals Dynamic of a nonautonomous two-species impulsive competitive system with infinite delays

2019 ◽  
Vol 17 (1) ◽  
pp. 776-794 ◽  
Author(s):  
Mengxin He ◽  
Zhong Li ◽  
Fengde Chen
Keyword(s):  
Comparison Theorem ◽  
Mathematical Analysis ◽  
Global Attractivity ◽  
Infinite Delay ◽  
Applied Mathematics ◽  
Almost Periodic ◽  
Competitive System ◽  
Dynamic Behaviors ◽  
Impulsive Equation ◽  
Infinite Delays

Abstract In this paper, we consider a nonautonomous two-species impulsive competitive system with infinite delays. By the impulsive comparison theorem and some mathematical analysis, we investigate the permanence, extinction and global attractivity of the system, as well as the influence of impulse perturbation on the dynamic behaviors of this system. For the logistic type impulsive equation with infinite delay, our results improve those of Xuxin Yang, Weibing Wang and Jianhua Shen [Permanence of a logistic type impulsive equation with infinite delay, Applied Mathematics Letters, 24(2011), 420-427]. For the corresponding nonautonomous two-species impulsive competitive system without delays, we discuss its permanence, extinction and global attractivity, which weaken and complement the results of Zhijun Liu and Qinglong Wang [An almost periodic competitive system subject to impulsive perturbations, Applied Mathematics and Computation, 231(2014), 377-385].

scholarly journals Dynamics of a Discrete Allelopathic Phytoplankton Model with Infinite Delays and Feedback Controls

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Liang Zhao ◽  
Bin Qin ◽  
Fengde Chen
Keyword(s):  
Comparison Theorem ◽  
Crucial Role ◽  
Sufficient Conditions ◽  
Lyapunov Functionals ◽  
Toxic Substances ◽  
Feedback Controls ◽  
Infinite Delays

A discrete allelopathic phytoplankton model with infinite delays and feedback controls is studied in this paper. By applying the discrete comparison theorem, a set of sufficient conditions which guarantees the permanence of the system is obtained. Also, by constructing some suitable discrete Lyapunov functionals, some sufficient conditions for the extinction of the system are obtained. Our results extend and supplement some known results and show that the feedback controls and toxic substances play a crucial role on the permanence and extinction of the system.

Asymptotic Behavior of a Stochastic Two-Species Competition System with Impulsive Effects

2018 ◽  
Vol 19 (5) ◽  
pp. 427-438
Author(s):  
Pan Wang ◽  
Bing Li ◽  
Yongkun Li
Keyword(s):  
Asymptotic Behavior ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Impulsive Effects ◽  
Species Competition ◽  
Stochastic Permanence ◽  
Competition System ◽  
Stochastic Boundedness ◽  
Dynamical Properties ◽  
Persistent In Mean

AbstractIn this paper, we consider a stochastic two-species competition system with impulsive effects. Some dynamical properties are investigated and sufficient conditions for the stochastic boundedness, stochastic permanence and global attractivity are established. Under some conditions, we conclude that the stochastic model is persistent in mean and extinction. An example is given to illustrate the main result.

scholarly journals Permanence and Positive Periodic Solutions of a Discrete Delay Competitive System

2010 ◽  
Vol 2010 ◽  
pp. 1-22 ◽  
Author(s):  
Wenjie Qin ◽  
Zhijun Liu
Keyword(s):  
Periodic Solutions ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Discrete Delay ◽  
Positive Periodic Solutions ◽  
Competitive System ◽  
Discrete Function ◽  
Species Population

A discrete time non-autonomous two-species competitive system with delays is proposed, which involves the influence of many generations on the density of species population. Sufficient conditions for permanence of the system are given. When the system is periodic, by using the continuous theorem of coincidence degree theory and constructing a suitable Lyapunov discrete function, sufficient conditions which guarantee the existence and global attractivity of positive periodic solutions are obtained. As an application, examples and their numerical simulations are presented to illustrate the feasibility of our main results.

Dynamics behaviors of a delayed competitive system in a random environment

2015 ◽  
Vol 08 (05) ◽  
pp. 1550062 ◽  
Author(s):  
Ronghua Tan ◽  
Huili Xiang ◽  
Yiping Chen ◽  
Zhijun Liu
Keyword(s):  
Global Existence ◽  
Random Environment ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Ultimate Boundedness ◽  
Unique Positive Solution ◽  
Competitive System ◽  
Stochastic Perturbations ◽  
Stochastically Ultimate Boundedness ◽  
White Noises

In the real world, the population systems are often subject to white noises and a system with such stochastic perturbations tends to be suitably modeled by stochastic differential equations. This paper is concerned with the dynamic behaviors of a delay stochastic competitive system. We first obtain the global existence of a unique positive solution of system. Later, we show that the solution of system will be stochastically ultimate boundedness. However, large noises may make the system extinct exponentially with probability one. Also, sufficient conditions for the global attractivity of system are established. Finally, illustrated examples are given to show the effectiveness of the proposed criteria.

scholarly journals Extinction of a two species non-autonomous competitive system with Beddington-DeAngelis functional response and the effect of toxic substances

2016 ◽  
Vol 14 (1) ◽  
pp. 1157-1173 ◽  
Author(s):  
Fengde Chen ◽  
Xiaoxing Chen ◽  
Shouying Huang
Keyword(s):  
Functional Response ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
The Other ◽  
Toxic Substances ◽  
Two Dimensional ◽  
Competitive System ◽  
Volterra Systems ◽  
Appl Math

AbstractA two species non-autonomous competitive phytoplankton system with Beddington-DeAngelis functional response and the effect of toxic substances is proposed and studied in this paper. Sufficient conditions which guarantee the extinction of a species and global attractivity of the other one are obtained. The results obtained here generalize the main results of Li and Chen [Extinction in two dimensional nonautonomous Lotka-Volterra systems with the effect of toxic substances, Appl. Math. Comput. 182(2006)684-690]. Numeric simulations are carried out to show the feasibility of our results.

PERMANENCE IN A DISCRETE n-SPECIES NON-AUTONOMOUS LOTKA–VOLTERRA COMPETITIVE SYSTEMS WITH INFINITE DELAYS AND FEEDBACK CONTROL

2007 ◽  
Vol 10 (04) ◽  
pp. 463-477 ◽  
Author(s):  
XIAOXING CHEN
Keyword(s):  
Feedback Control ◽  
Sufficient Conditions ◽  
Competitive Systems ◽  
Infinite Delays

In this paper, we deal with a discrete n-species non-autonomous Lotka–Volterra competitive systems with infinite delays and feedback control, obtain sufficient conditions for the permanence of the systems.

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