Existence of Periodic Solutions for a Delayed Ratio-Dependent Three-Species Predator-Prey Diffusion System on Time Scales

• Main Author: Liu Zhenjie
• Format: Article
• Language: English
• Published: SpringerOpen 2009-01-01
• Series: Advances in Difference Equations
• Online Access: http://www.advancesindifferenceequations.com/content/2009/141589

<p/> <p>This paper investigates the existence of periodic solutions of a ratio-dependent predator-prey diffusion system with Michaelis-Menten functional responses and time delays in a two-patch environment on time scales. By using a continuation theorem based on coincidence degree theory, we obtain suffcient criteria for the existence of periodic solutions for the system. Moreover, when the time scale <inline-formula><graphic file="1687-1847-2009-141589-i1.gif"/></inline-formula> is chosen as <inline-formula><graphic file="1687-1847-2009-141589-i2.gif"/></inline-formula> or <inline-formula><graphic file="1687-1847-2009-141589-i3.gif"/></inline-formula>, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the methods are unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations.</p>