scholarly journals Positive periodic solution for a two-species ratio-dependent predator–prey system with time delay and impulse

2007 ◽  
Vol 325 (1) ◽  
pp. 715-723 ◽  
Author(s):  
Xiangsen Liu ◽  
Gang Li ◽  
Guilie Luo
Keyword(s):  
Periodic Solution ◽  
Time Delay ◽  
Positive Periodic Solution ◽  
Predator Prey ◽  
Prey System ◽  
Ratio Dependent ◽  
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.

scholarly journals Periodic solutions of a two-species ratio-dependent predator-prey system with time delay in a two-patch environment

2003 ◽  
Vol 45 (2) ◽  
pp. 233-244 ◽  
Author(s):  
Zhengqiu Zhang ◽  
Zhicheng Wang
Keyword(s):  
Periodic Solution ◽  
Time Delay ◽  
Periodic Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solution ◽  
Sufficient Condition ◽  
Predator Prey ◽  
Prey System ◽  
System With Time Delay

AbstractBy using the continuation theorem of coincidence degree theory, a sufficient condition is obtained for the existence of a positive periodic solution of a predator-prey diffusion system.

Dynamics of a non-autonomous ratio-dependent predator—prey system

2003 ◽  
Vol 133 (1) ◽  
pp. 97-118 ◽  
Author(s):  
Meng Fan ◽  
Qian Wang ◽  
Xingfu Zou
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Positive Periodic Solution ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Predator Prey ◽  
Prey System ◽  
Autonomous Case ◽  
Positive Almost Periodic Solution ◽  
Ratio Dependent

We investigate a non-autonomous ratio-dependent predator–prey system, whose autonomous versions have been analysed by several authors. For the general non-autonomous case, we address such properties as positive invariance, permanence, non-persistence and the globally asymptotic stability for the system. For the periodic and almost-periodic cases, we obtain conditions for existence, uniqueness and stability of a positive periodic solution, and a positive almost-periodic solution, respectively.

scholarly journals Periodicity in a ratio-dependent predator-prey system with stage structure for predator

2005 ◽  
Vol 2005 (2) ◽  
pp. 153-169 ◽  
Author(s):  
Fengde Chen
Keyword(s):  
Periodic Solution ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Stage Structure ◽  
Positive Periodic Solution ◽  
Positive Periodic Solutions ◽  
Priori Estimate ◽  
Predator Prey ◽  
Prey System ◽  
Ratio Dependent

With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of a delayed ratio-dependent predator-prey system with stage structure for predator. The approach involves some new technique of priori estimate. For the system without delay, by constructing a suitable Lyapunov function, some sufficient conditions which guarantee the existence of a unique global attractive positive periodic solution are obtained. Those results have further applications in population dynamics.

Periodic Solution of a Class Predator-Prey System with Rate Stocking and Time Delay

2013 ◽  
Vol 291-294 ◽  
pp. 2412-2415
Author(s):  
Hui Li ◽  
Yi Fei Wang
Keyword(s):  
Periodic Solution ◽  
Time Delay ◽  
Periodic System ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solution ◽  
Coincidence Degree Theory ◽  
Predator Prey ◽  
Prey System

In this paper, we investigate of a class of predator-prey system with rate stocking and time delay, the existence positive periodic solution by using coincidence degree theory. We obtain the sufficient conditions which guarantee existence of the positive periodic solution of the periodic system. Some new results obtained.

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