Dynamic Analysis of a Predator-Prey System with Time Delay and Pulse Control

2018 ◽  
Vol 07 (08) ◽  
pp. 987-999
Author(s):  
晶 杨
Keyword(s):  
Time Delay ◽  
Dynamic Analysis ◽  
Pulse Control ◽  
Predator Prey ◽  
Prey System ◽  
System With Time Delay

A stage-structured predator-prey system with time delay

2009 ◽  
Vol 33 (1-2) ◽  
pp. 267-281 ◽  
Author(s):  
Lingshu Wang ◽  
Rui Xu ◽  
Guanghui Feng
Keyword(s):  
Time Delay ◽  
Predator Prey ◽  
Prey System ◽  
System With Time Delay

POSITIVE PERIODIC SOLUTION FOR A GAUSE-TYPE RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH DIFFUSION AND TIME DELAY

2008 ◽  
Vol 01 (03) ◽  
pp. 339-354 ◽  
Author(s):  
XIAOQUAN DING ◽  
YUANYUAN WANG
Keyword(s):  
Periodic Solution ◽  
Time Delay ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solution ◽  
Continuation Theorem ◽  
Predator Prey ◽  
Prey System ◽  
Ratio Dependent ◽  
System With Time Delay

A two-species Gause-type ratio-dependent predator-prey system with time delay in a two-patch environment is investigated. By using a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of periodic solution for the system. As corollaries, some applications are listed. In particular, our results extend and improve some known results.

Rank one chaos in periodically kicked Lotka–Volterra predator–prey system with time delay

2016 ◽  
Vol 85 (2) ◽  
pp. 797-811 ◽  
Author(s):  
Zhiliang Luo ◽  
Yiping Lin ◽  
Yunxian Dai
Keyword(s):  
Time Delay ◽  
Predator Prey ◽  
Prey System ◽  
Rank One ◽  
System With Time Delay

Rank One Strange Attractors in Periodically Kicked Predator–Prey System with Time-Delay

2016 ◽  
Vol 26 (07) ◽  
pp. 1640114 ◽  
Author(s):  
Wenjie Yang ◽  
Yiping Lin ◽  
Yunxian Dai ◽  
Huitao Zhao
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Strange Attractors ◽  
Periodic Force ◽  
Delayed Systems ◽  
Predator Prey ◽  
Prey System ◽  
Rank One ◽  
Delayed System ◽  
System With Time Delay

This paper is devoted to the study of the problem of rank one strange attractor in a periodically kicked predator–prey system with time-delay. Our discussion is based on the theory of rank one maps formulated by Wang and Young. Firstly, we develop the rank one chaotic theory to delayed systems. It is shown that strange attractors occur when the delayed system undergoes a Hopf bifurcation and encounters an external periodic force. Then we use the theory to the periodically kicked predator–prey system with delay, deriving the conditions for Hopf bifurcation and rank one chaos along with the results of numerical simulations.

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