Periodic Solutions for a Semi‐Ratio‐Dependent Predator‐Prey System with Delays on Time Scales | Zendy

Xiaoquan Ding | Zendy; Gaifang Zhao | Zendy

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Periodic Solutions for a Semi‐Ratio‐Dependent Predator‐Prey System with Delays on Time Scales

Author(s) -

Xiaoquan Ding,

Gaifang Zhao

Publication year - 2012

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2012/928704

Subject(s) - type (biology) , mathematics , functional response , coincidence , monotonic function , sigmoid function , logistic function , predation , continuation , comparison theorem , control theory (sociology) , mathematical analysis , predator , computer science , statistics , ecology , biology , programming language , medicine , alternative medicine , control (management) , pathology , artificial intelligence , artificial neural network , machine learning

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

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