Existence of Periodic Solutions in Predator Prey and Competition Dynamic Systems


In this paper, we systematically explore the periodicity of some dynamic equations on time scales, which incorporate as special cases many population models (e.g., predator-prey systems and competition systems) in mathematical biology governed by differential equations and difference equations. Easily verifiable sufficient criteria are established for the existence of periodic solutions of such dynamic equations, which generalize many known results for continuous and discrete population models when the time scale View the MathML source is chosen as View the MathML source or View the MathML source, respectively. The main approach is based on a continuation theorem in coincidence degree theory, which has been extensively applied in studying existence problems in differential equations and difference equations but rarely applied in dynamic equations on time scales. This study shows that it is unnecessary to explore the existence of periodic solutions of continuous and discrete population models in separate ways. One can unify such studies in the sense of dynamic equations on general time scales.


Mathematics and Statistics

Keywords and Phrases

Beddington-DeAngelis response; Coincidence degree; Competition system; Gilpin-Ayala system; Holling-type response; Periodic solution; Predator-prey system; Time scales

Document Type

Article - Journal

Document Version


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© 2006 Elsevier, All rights reserved.

Publication Date

01 Jan 2006