Periodic Solutions for a Delayed Predator-Prey System with Harvesting Terms and Holling IV Functional Responses on Time Scales*

2013 ◽  
Author(s):  
Pan Wang ◽  
Yongkun Li
Keyword(s):  
Periodic Solutions ◽  
Time Scales ◽  
Functional Responses ◽  
Predator Prey ◽  
Prey System

scholarly journals Periodic Solutions for a Semi-Ratio-Dependent Predator-Prey System with Delays on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Xiaoquan Ding ◽  
Gaifang Zhao
Keyword(s):  
Periodic Solutions ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Functional Responses ◽  
Predator Prey ◽  
Prey System ◽  
Special Cases ◽  
Existence Of Periodic Solutions ◽  
Ratio Dependent

This paper is devoted to the existence of periodic solutions for a semi-ratio-dependent predator-prey system with time delays on time scales. With the help of a continuation theorem based on coincidence degree theory, we establish necessary and sufficient conditions for the existence of periodic solutions. Our results show that for the most monotonic prey growth such as the logistic, the Gilpin, and the Smith growth, and the most celebrated functional responses such as the Holling type, the sigmoidal type, the Ivlev type, the Monod-Haldane type, and the Beddington-DeAngelis type, the system always has at least one periodic solution. Some known results are shown to be special cases of the present paper.

scholarly journals Multiple Periodic Solutions of Delayed Predator-Prey Systems with Type IV Functional Responses on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Shengbin Yu ◽  
Haihui Wu ◽  
Jiangbin Chen
Keyword(s):  
Periodic Solutions ◽  
Time Scales ◽  
Coincidence Degree ◽  
Continuation Theorem ◽  
Positive Periodic Solutions ◽  
Functional Responses ◽  
Predator Prey ◽  
Type Iv ◽  
Multiple Periodic Solutions

With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the existence of multiple positive periodic solutions of delayed predator-prey systems with type IV functional responses on time scales. Our results not only unify the existing ones but also widen the range of applications.

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.

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