A Predator-Prey System with Mutual Interference Concerning IPM

2011 ◽  
Author(s):  
Shun-yi Li ◽  
Xian-gui Xue
Keyword(s):  
Mutual Interference ◽  
Predator Prey ◽  
Prey System

scholarly journals Dynamic Behavior of Positive Solutions for a Leslie Predator-Prey System with Mutual Interference and Feedback Controls

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Cong Zhang ◽  
Nan-jing Huang ◽  
Chuan-xian Deng
Keyword(s):  
Global Attractivity ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Mutual Interference ◽  
Periodic Case ◽  
Feedback Controls ◽  
Predator Prey ◽  
Prey System ◽  
Inequality Theory ◽  
Nonautonomous Case

We consider a Leslie predator-prey system with mutual interference and feedback controls. For general nonautonomous case, by using differential inequality theory and constructing a suitable Lyapunov functional, we obtain some sufficient conditions which guarantee the permanence and the global attractivity of the system. For the periodic case, we obtain some sufficient conditions which guarantee the existence, uniqueness, and stability of a positive periodic solution.

scholarly journals Existence of Positive Periodic Solutions for a Predator-Prey System of Holling Type IV Function Response with Mutual Interference and Impulsive Effects

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Haidong Liu ◽  
Fanwei Meng
Keyword(s):  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Mutual Interference ◽  
Impulsive Effects ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Type Iv ◽  
Prey System ◽  
Predator Prey Models

We investigate the existence of periodic solutions for a predator-prey system with Holling function response and mutual interference. Our model is more general than others since it has both Holling type IV function and impulsive effects. With some new analytical tricks and the continuation theorem in coincidence degree theory proposed by Gaines and Mawhin, we obtain a set of sufficient conditions on the existence of positive periodic solutions for such a system. In addition, in the remark, we point out some minor errors which appeared in the proof of theorems in some published papers with relevant predator-prey models. An example is given to illustrate our results.

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