scholarly journals Persistence and global stability of positive periodic solutions of three species food chains with omnivory

2006 ◽  
Vol 324 (1) ◽  
pp. 397-408 ◽  
Author(s):  
Shu-Rong Zhou ◽  
Wan-Tong Li ◽  
Gang Wang
Keyword(s):  
Global Stability ◽  
Periodic Solutions ◽  
Food Chains ◽  
Positive Periodic Solutions

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

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Wenjie Qin ◽  
Zhijun Liu ◽  
Yiping Chen
Keyword(s):  
Global Stability ◽  
Numerical Simulations ◽  
Periodic Solutions ◽  
Positive Periodic Solutions ◽  
Competitive System ◽  
Dynamic Behaviors ◽  
System A ◽  
Analytical Results

We consider the dynamic behaviors of a discrete competitive system. A good understanding of the permanence, existence, and global stability of positive periodic solutions is gained. Numerical simulations are also presented to substantiate the analytical results.

scholarly journals 2 N POSITIVE PERIODIC SOLUTIONS TO N SPECIES NON‐AUTONOMOUS LOTKA‐VOLTERRA UNIDIRECTIONAL FOOD CHAINS WITH HARVESTING TERMS

2010 ◽  
Vol 15 (3) ◽  
pp. 313-326 ◽  
Author(s):  
Yongkun Li ◽  
Kaihong Zhao
Keyword(s):  
Periodic Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Food Chains ◽  
Positive Periodic Solutions ◽  
Mawhin Continuation Theorem

By using the Mawhin continuation theorem of coincidence degree theory and some results on inequalities, we establish the existence of 2 n positive periodic solutions for n species non‐autonomous Lotka‐Volterra unidirectional food chains with harvesting terms. Two examples are given to illustrate the effectiveness of our results.

scholarly journals Global Positive Periodic Solutions for Periodic Two-Species Competitive Systems with Multiple Delays and Impulses

2014 ◽  
Vol 2014 ◽  
pp. 1-23 ◽  
Author(s):  
Zhenguo Luo ◽  
Liping Luo ◽  
Liu Yang ◽  
Yunhui Zeng
Keyword(s):  
Global Stability ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Multiple Delays ◽  
Positive Periodic Solutions ◽  
Analysis Techniques ◽  
Competitive Systems ◽  
Sufficiency Theorems

A set of easily verifiable sufficient conditions are derived to guarantee the existence and the global stability of positive periodic solutions for two-species competitive systems with multiple delays and impulses, by applying some new analysis techniques. This improves and extends a series of the well-known sufficiency theorems in the literature about the problems mentioned previously.

scholarly journals Existence and global stability of positive periodic solutions of a discrete delay competition system

2003 ◽  
Vol 2003 (38) ◽  
pp. 2401-2413 ◽  
Author(s):  
Hai-Feng Huo ◽  
Wan-Tong Li
Keyword(s):  
Lyapunov Function ◽  
Global Stability ◽  
Periodic Solutions ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Discrete Delay ◽  
Positive Periodic Solutions ◽  
Competition System ◽  
Standard Procedures ◽  
Topological Degree Method

The existence and the global stability of positive periodic solutions of a discrete competition model is studied. The model incorporates time delays and allows for a fluctuating environment. By means of some standard procedures of the topological degree method and the construction of a suitable Lyapunov function, sufficient conditions are obtained to ensure the existence and the global stability of positive periodic solutions of the above systems.

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