The dynamics of a mutual interference age structured predator–prey model with time delay and impulsive perturbations on predators

2010 ◽  
Vol 216 (1) ◽  
pp. 308-316 ◽  
Author(s):  
Guanghu Zhu ◽  
Xinzhu Meng ◽  
Lansun Chen
Keyword(s):  
Time Delay ◽  
Mutual Interference ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Impulsive Perturbations ◽  
Age Structured

scholarly journals Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xinze Lian ◽  
Shuling Yan ◽  
Hailing Wang
Keyword(s):  
Time Delay ◽  
Pattern Formation ◽  
Turing Instability ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Prey Model ◽  
Diffusion Controlled ◽  
The Stability ◽  
Self Replication

We consider the effect of time delay and cross diffusion on the dynamics of a modified Leslie-Gower predator-prey model incorporating a prey refuge. Based on the stability analysis, we demonstrate that delayed feedback may generate Hopf and Turing instability under some conditions, resulting in spatial patterns. One of the most interesting findings is that the model exhibits complex pattern replication: the model dynamics exhibits a delay and diffusion controlled formation growth not only to spots, stripes, and holes, but also to spiral pattern self-replication. The results indicate that time delay and cross diffusion play important roles in pattern formation.

scholarly journals Uniformly Strong Persistence for a Delayed Predator-Prey Model

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Changjin Xu ◽  
Yuanfu Shao ◽  
Peiluan Li
Keyword(s):  
Time Delay ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Asymptotically Periodic

An asymptotically periodic predator-prey model with time delay is investigated. Some sufficient conditions for the uniformly strong persistence of the system are obtained. Our result is an important complementarity to the earlier results.

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