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.

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.

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.

scholarly journals Existence of Positive Periodic Solutions for a Nonautonomous Generalized Predator-Prey System with Time Delay in Two-Patch Environment

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Huilan Wang ◽  
Zhengqiu Zhang ◽  
Weiping Zhou
Keyword(s):  
Periodic Solutions ◽  
Topological Degree ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Prey System ◽  
System With Time Delay ◽  
Function Matrix

By using continuation theorem of coincidence degree theory, sufficient conditions of the existence of positive periodic solutions are obtained for a generalized predator-prey system with diffusion and delays. In this paper, we construct a V-function to make the prior estimation for periodic solutions, which makes the discussion more concise. Moreover, to compute the mapping's topological degree, a polynomial function matrix is constructed straightforwardly as a homotopic mapping for the generalized one, which improves the methods of computation on topological degree for a generalized mapping.

PERIODICITY IN AN STAGE-STRUCTURED THREE-SPECIES PREDATOR–PREY SYSTEM WITH BEDDINGTON–DEANGELIS AND HOLLINF IV FUNCTIONAL RESPONSE

2012 ◽  
Vol 05 (02) ◽  
pp. 1250031
Author(s):  
Changjin Xu ◽  
Maoxin Liao
Keyword(s):  
Functional Response ◽  
Lyapunov Functional ◽  
Global Attractivity ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solution ◽  
Sufficient Condition ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Prey System

In this paper, by using the continuation theorem of coincidence degree theory, a sufficient condition of existence of positive periodic solutions is obtained for an stage-structured three-species predator–prey system with Beddington–DeAngelis and Holling IV functional response. By constructing a suitable Lyapunov functional, the uniqueness and global attractivity of the positive periodic solution are presented. Our result is a good complement to the earlier publications.

EXISTENCE FOR PERIODIC SOLUTIONS OF A RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH TIME-VARYING DELAYS ON TIME SCALES

2010 ◽  
Vol 08 (03) ◽  
pp. 227-233
Author(s):  
HUIJUAN LI ◽  
ANPING LIU ◽  
ZUTAO HAO
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Functional Response ◽  
Time Scales ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Time Varying ◽  
Predator Prey ◽  
Prey System ◽  
Ratio Dependent

In this paper, by using the continuation theorem of coincidence degree theory we study the existence of periodic solution for a two-species ratio-dependent predator-prey system with time-varying delays and Machaelis–Menten type functional response on time scales. Some new results are obtained.

scholarly journals A Time Delay Predator-Prey System with Three-Stage-Structure

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qiaoqin Gao ◽  
Zhen Jin
Keyword(s):  
Coincidence Degree ◽  
Degree Theory ◽  
Stage Structure ◽  
Positive Periodic Solution ◽  
Sufficient Condition ◽  
Discrete Delay ◽  
Predator Species ◽  
Predator Prey ◽  
Prey System ◽  
Three Stages

A predator-prey system was studied that has a discrete delay, stage-structure, and Beddington-DeAngelis functional response, where predator species has three stages, immature, mature, and old age stages. By using of Mawhin's continuous theorem of coincidence degree theory, a sufficient condition is obtained for the existence of a positive periodic solution.

scholarly journals Multiple Positive Periodic Solutions for a Gilpin-Ayala Competition Predator-Prey System with Harvesting Terms

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Yongzhi Liao ◽  
Yongkun Li ◽  
Xiaoyan Dou
Keyword(s):  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Positive Periodic Solutions ◽  
Mawhin’S Continuation Theorem ◽  
Predator Prey ◽  
Prey System

By applying Mawhin’s continuation theorem of coincidence degree theory, we study the existence of multiple positive periodic solutions for a Gilpin-Ayala competition predator-prey system with harvesting terms and obtain some sufficient conditions for the existence of multiple positive periodic solutions for the system under consideration. The result of this paper is completely new. An example is employed to illustrate our result.

PERIODIC SOLUTIONS OF A DISCRETE TIME NONAUTONOMOUS TWO-SPECIES MUTUALISTIC SYSTEM WITH DELAYS

2006 ◽  
Vol 09 (01n02) ◽  
pp. 87-98 ◽  
Author(s):  
ZHIJUN LIU ◽  
LANSUN CHEN
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Discrete Time ◽  
Coincidence Degree ◽  
Positive Periodic Solution ◽  
Sufficient Condition ◽  
Species Population

We establish a discrete time non-autonomous two-species mutualistic system with delays by considering the influence of many generations on the density of species population. With the help of the method of coincidence degree and some techniques, an easily verifiable sufficient condition is derived for the existence of at least one positive periodic solution of the above system. Biological interpretations of the main result are also given.

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