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 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 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.

PERMANENCE IN NONAUTONOMOUS DISCRETE LOTKA–VOLTERRA n-SPECIES COMPETITIVE SYSTEMS WITH PURE-DELAYS AND FEEDBACK CONTROLS

2013 ◽  
Vol 24 (07) ◽  
pp. 1350053 ◽  
Author(s):  
AHMADJAN MUHAMMADHAJI ◽  
ZHIDONG TENG ◽  
LINFEI NIE
Keyword(s):  
Sufficient Conditions ◽  
Lyapunov Functionals ◽  
Feedback Controls ◽  
Volterra Type ◽  
Competitive Systems ◽  
Analysis Technique

The paper discusses nonautonomous discrete Lotka–Volterra type n-species competitive systems with pure-delays and feedback controls. New sufficient conditions for which a part of the n-species remains permanent and others is driven to extinction are established by using the method of multiple discrete Lyapunov functionals and introducing new analysis technique. Our results show that the feedback controls cannot influence the permanence of species.

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.

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 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 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.

scholarly journals The Extinction of a Non-Autonomous Allelopathic Phytoplankton Model with Nonlinear Inter-Inhibition Terms and Feedback Controls

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 173 ◽  
Author(s):  
Liang Zhao ◽  
Fengde Chen ◽  
Saixi Song ◽  
Guizhen Xuan
Keyword(s):  
Differential Equation ◽  
Comparison Theorem ◽  
Difference Equations ◽  
Crucial Role ◽  
Sufficient Conditions ◽  
Toxic Substances ◽  
Competitive System ◽  
Feedback Controls

A non-autonomous allelopathic phytoplankton model with nonlinear inter-inhibition terms and feedback controls is studied in this paper. Based on the comparison theorem of differential equation, some sufficient conditions for the permanence of the system are obtained. We study the extinction of one of the species by using some suitable Lyapunov type extinction function. Our analyses extend those of Xie et al. (Extinction of a two species competitive system with nonlinear inter-inhibition terms and one toxin producing phytoplankton. Advances in Difference Equations, 2016, 2016, 258) and show that the feedback controls and toxic substances have no effect on the permanence of the system but play a crucial role on the extinction of the system. Some known results are extended.

scholarly journals Determination of positive realizations with reduced numbers of delays or without delays for discrete-time linear systems

2012 ◽  
Vol 22 (4) ◽  
pp. 451-465 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Transfer Function ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Diagram Method ◽  
State Variable ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Time Linear

A new modified state variable diagram method is proposed for determination of positive realizations with reduced numbers of delays and without delays of linear discrete-time systems for a given transfer function. Sufficient conditions for the existence of the positive realizations of given proper transfer function are established. It is shown that there exists a positive realization with reduced numbers of delays if there exists a positive realization without delays but with greater dimension. The proposed methods are demonstrated on a numerical example.

scholarly journals The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 865
Author(s):  
Jialin Chen ◽  
Xiaqing He ◽  
Fengde Chen
Keyword(s):  
Discrete Time ◽  
Food Resource ◽  
Sufficient Conditions ◽  
Iteration Scheme ◽  
Predator Species ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Fear Effect ◽  
Prey System ◽  
Trivial Equilibrium

A discrete-time predator–prey system incorporating fear effect of the prey with the predator has other food resource is proposed in this paper. The trivial equilibrium and the predator free equilibrium are both unstable. A set of sufficient conditions for the global attractivity of prey free equilibrium and interior equilibrium are established by using iteration scheme and the comparison principle of difference equations. Our study shows that due to the fear of predation, the prey species will be driven to extinction while the predator species tends to be stable since it has other food resource, i.e., the prey free equilibrium may be globally stable under some suitable conditions. Numeric simulations are provided to illustrate the feasibility of the main results.

Sign in / Sign up

Export Citation Format

Share Document