scholarly journals Permanence of a Discrete n-Species Schoener Competition System with Time Delays and Feedback Controls

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Xuepeng Li ◽  
Wensheng Yang
Keyword(s):  
Time Delays ◽  
Feedback Controls ◽  
Competition System

scholarly journals Feedback Control Variables Have No Influence on the Permanence of a Discreten-Species Schoener Competition System with Time Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Qianqian Su ◽  
Na Zhang
Keyword(s):  
Feedback Control ◽  
Numerical Simulations ◽  
Time Delays ◽  
Feedback Controls ◽  
Control Variables ◽  
Difference Inequality ◽  
Competition System ◽  
Inequality Theory

We consider a discreten-species Schoener competition system with time delays and feedback controls. By using difference inequality theory, a set of conditions which guarantee the permanence of system is obtained. The results indicate that feedback control variables have no influence on the persistent property of the system. Numerical simulations show the feasibility of our results.

scholarly journals Positive Periodic Solutions of Cooperative Systems with Delays and Feedback Controls

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Tursuneli Niyaz ◽  
Ahmadjan Muhammadhaji
Keyword(s):  
Periodic Solutions ◽  
Continuous Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Positive Periodic Solutions ◽  
Feedback Controls ◽  
Volterra Systems

This paper studies a class of periodicnspecies cooperative Lotka-Volterra systems with continuous time delays and feedback controls. Based on the continuation theorem of the coincidence degree theory developed by Gaines and Mawhin, some new sufficient conditions on the existence of positive periodic solutions are established.

scholarly journals Dynamics in a ratio-dependent Lotka–Volterra competitive-competitive-cooperative system with feedback controls and delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmadjan Muhammadhaji ◽  
Azhar Halik ◽  
Hong-Li Li
Keyword(s):  
Time Delays ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Comparison Method ◽  
Cooperative System ◽  
Functional Responses ◽  
Feedback Controls ◽  
Lyapunov Function Method ◽  
Inequality Techniques ◽  
Ratio Dependent

AbstractThis study investigates the dynamical behavior of a ratio-dependent Lotka–Volterra competitive-competitive-cooperative system with feedback controls and delays. Compared with previous studies, both ratio-dependent functional responses and time delays are considered. By employing the comparison method, the Lyapunov function method, and useful inequality techniques, some sufficient conditions on the permanence, periodic solution, and global attractivity for the considered system are derived. Finally, a numerical example is also presented to validate the practicability and feasibility of our proposed results.

scholarly journals Dynamics in a Delayed Competition System on a Weighted Network

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yaohua Tong ◽  
Xiaoling Wang
Keyword(s):  
Steady State ◽  
Time Delays ◽  
Complex Dynamics ◽  
Sufficient Conditions ◽  
Weighted Network ◽  
Competition System ◽  
Numerical Examples ◽  
Competitive Systems ◽  
Positive Steady States ◽  
The Stability

In this paper, we study the stability of positive steady states in a delayed competition system on a weighted network, which does not satisfy the comparison principle appealing to classical competitive systems. By introducing some auxiliary equations and constructing proper contracting rectangles, we present some sufficient conditions on the stability of the unique positive steady state. Moreover, some numerical examples are given to explore the complex dynamics of this nonmonotone model, which implies the nontrivial roles of weights and time delays.

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