A stage structured predator-prey system with delay dependent parameters

2013 ◽  
Author(s):  
Zou Xiaojian ◽  
Hu Baoan ◽  
Liu Junfeng
Keyword(s):  
Predator Prey ◽  
System With Delay ◽  
Prey System ◽  
Delay Dependent

The diffusive Lotka–Volterra predator–prey system with delay

2015 ◽  
Vol 270 ◽  
pp. 30-40 ◽  
Author(s):  
K.S. Al Noufaey ◽  
T.R. Marchant ◽  
M.P. Edwards
Keyword(s):  
Predator Prey ◽  
System With Delay ◽  
Prey System

BIFURCATION ANALYSIS OF A LOGISTIC PREDATOR–PREY SYSTEM WITH DELAY

2016 ◽  
Vol 57 (4) ◽  
pp. 445-460
Author(s):  
CANAN ÇELİK ◽  
GÖKÇEN ÇEKİÇ
Keyword(s):  
Delay Time ◽  
Critical Values ◽  
Normal Form Theory ◽  
Predator Prey ◽  
System With Delay ◽  
Prey System ◽  
Form Theory ◽  
Bifurcating Periodic Solution ◽  
Centre Manifold Theorem ◽  
Theoretical Results

We consider a coupled, logistic predator–prey system with delay. Mainly, by choosing the delay time${\it\tau}$as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay time${\it\tau}$passes some critical values. Based on the normal-form theory and the centre manifold theorem, we also derive formulae to obtain the direction, stability and the period of the bifurcating periodic solution at critical values of ${\it\tau}$. Finally, numerical simulations are investigated to support our theoretical results.

Global qualitative analysis for a predator–prey system with delay☆

2007 ◽  
Vol 32 (4) ◽  
pp. 1582-1596 ◽  
Author(s):  
Chengjun Sun ◽  
Maoan Han ◽  
Yiping Lin ◽  
Yuanyuan Chen
Keyword(s):  
Qualitative Analysis ◽  
Predator Prey ◽  
System With Delay ◽  
Prey System

scholarly journals Relaxation Oscillations in a System with Delays Modeling the Predator-Prey Problem

2015 ◽  
Vol 20 (1) ◽  
pp. 52-98 ◽  
Author(s):  
S. A. Kaschenko
Keyword(s):  
Asymptotic Analysis ◽  
System Dynamics ◽  
Asymptotic Method ◽  
Relaxation Oscillations ◽  
Predator Prey ◽  
One Dimensional ◽  
System With Delay ◽  
Prey System ◽  
One Dimensional Maps ◽  
Biological Nature

A new asymptotic method for investigating complex relaxation oscillations of a system with delay was offered. Applying it, we can reduce the problem of predator-prey system dynamics to problem of one-dimensional maps analysis. Some conclusions of biological nature based on the asymptotic analysis were made. 

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