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.
M. Fan et al., "Existence of Periodic Solutions in Predator Prey and Competition Dynamic Systems," Non Linear Analysis: Real World Applications, Elsevier, Jan 2006.
The definitive version is available at http://dx.doi.org/10.1016/j.nonrwa.2005.11.002
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
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