Periodicity and stability for a Lotka–Volterra type competition system with feedback controls and deviating arguments

2011 ◽  
Vol 74 (9) ◽  
pp. 2916-2928 ◽  
Author(s):  
Jurang Yan ◽  
Guirong Liu
Keyword(s):  
Feedback Controls ◽  
Volterra Type ◽  
Deviating Arguments ◽  
Competition 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 Permanence in a Discrete Mutualism Model with Infinite Deviating Arguments and Feedback Controls

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Changjin Xu ◽  
Yusen Wu
Keyword(s):  
Sufficient Conditions ◽  
Feedback Controls ◽  
Difference Inequality ◽  
Deviating Arguments ◽  
Inequality Theory ◽  
The Difference ◽  
Mutualism Model

We propose and deal with a discrete mutualism model with infinite deviating arguments and feedback controls. Sufficient conditions which guarantee the permanence of the system are obtained by using the difference inequality theory. The paper ends with brief conclusions.

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.

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