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 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.

Almost periodic solutions of nonautonomous Lotka–Volterra competitive systems with dominated delays

2015 ◽  
Vol 08 (02) ◽  
pp. 1550019 ◽  
Author(s):  
Chunhua Feng ◽  
Jianmin Huang
Keyword(s):  
Periodic Solutions ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Volterra System ◽  
Volterra Type ◽  
Competitive Systems

In this paper, a class of nonautonomous Lotka–Volterra type multispecies competitive systems with delays is studied. By employing Lyapunov functional, some sufficient conditions to guarantee the existence of almost periodic solutions for the Lotka–Volterra system are obtained.

PERSISTENCE, EXTINCTION AND STABILITY FOR NONLINEAR PLANKTON ALLELOPATHY MODEL WITH DELAYED NEGATIVE FEEDBACKS

2012 ◽  
Vol 05 (02) ◽  
pp. 1250027 ◽  
Author(s):  
YAN-PING LIU ◽  
ZHI-XUE LUO
Keyword(s):  
Numerical Simulations ◽  
Sufficient Conditions ◽  
Lyapunov Functionals ◽  
Analysis Method ◽  
Average Value ◽  
Competitive Systems ◽  
Comparison Argument ◽  
Negative Feedbacks ◽  
Plankton Allelopathy ◽  
The Stability

By the techniques of comparison argument and Lyapunov-like functionals, some criteria about persistence and extinction of the species are obtained. And then, with the help of constructing Lyapunov functionals and some new analysis method, sufficient conditions, provided with the form of average value of a function, to guarantee the stability of the system are derived. Finally, some examples together with their numerical simulations show the feasibility of these main results. Our conclusions are different from many existing forms for nonlinear competitive systems.

The Permanence of a Ratio-Dependent Lotka-Volterra Predator-Prey Model with Feedback Control

2013 ◽  
Vol 765-767 ◽  
pp. 327-330
Author(s):  
Chang You Wang ◽  
Xiang Wei Li ◽  
Hong Yuan
Keyword(s):  
Feedback Control ◽  
Sufficient Conditions ◽  
Functional Responses ◽  
Feedback Controls ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Analysis Technique ◽  
Ratio Dependent

This paper is concerned with a Lotka-Volterra predator-prey system with ratio-dependent functional responses and feedback controls. By developing a new analysis technique, we establish the sufficient conditions which guarantee the permanence of the model.

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 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.

PERMANENCE OF A DISCRETE n-SPECIES LOTKA–VOLTERRA TYPE FOOD-CHAIN SYSTEM WITH FEEDBACK CONTROLS AND TIME DELAYS

2008 ◽  
Vol 01 (03) ◽  
pp. 299-311 ◽  
Author(s):  
XUMING HUANG ◽  
WENSHENG YANG ◽  
XUEPENG LI
Keyword(s):  
Difference Equation ◽  
Comparison Theorem ◽  
Food Chain ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Feedback Controls ◽  
Volterra Type ◽  
Chain System

In this paper, a discrete n-species Lotka–Volterra type food-chain system with time delays and feedback controls is proposed. By applying the comparison theorem of difference equation, sufficient conditions are obtained for the permanence of the system.

scholarly journals Global attractivity and extinction for Lotka–Volterra systems with infinite delay and feedback controls

2015 ◽  
Vol 145 (2) ◽  
pp. 301-330 ◽  
Author(s):  
Teresa Faria ◽  
Yoshiaki Muroya
Keyword(s):  
Global Attractivity ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Weak Form ◽  
Volterra Model ◽  
Delay Effect ◽  
Feedback Controls ◽  
Competitive Systems ◽  
Volterra Systems ◽  
Multiple Species

The paper deals with a multiple species Lotka–Volterra model with infinite distributed delays and feedback controls, for which we assume a weak form of diagonal dominance of the instantaneous negative intra-specific terms over the infinite delay effect in both the population variables and controls. General sufficient conditions for the existence and attractivity of a saturated equilibrium are established. When the saturated equilibrium is on the boundary of , sharper criteria for the extinction of all or part of the populations are given. While the literature usually treats the case of competitive systems only, here no restrictions on the signs of the intra- and inter-specific delayed terms are imposed. Moreover, our technique does not require the construction of Lyapunov functionals.

scholarly journals Permanence and Almost Periodic Solution for an Enterprise Cluster Model Based on Ecology Theory with Feedback Controls on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Yuanhong Zhi ◽  
Zunling Ding ◽  
Yongkun Li
Keyword(s):  
Periodic Solution ◽  
Time Scales ◽  
Cluster Model ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Feedback Controls ◽  
Competition And Cooperation ◽  
Enterprise Cluster

We present a model with feedback controls based on ecology theory, which effectively describes the competition and cooperation of enterprise cluster in real economic environments. Applying the comparison theorem of dynamic equations on time scales and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and the existence of uniformly asymptotically stable almost periodic solution of the system are obtained.

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