School of Mathematics and Computer, Harbin University, Harbin, Heilongjiang 150086, China
Copyright © 2009 Zhenjie Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 is chosen as or , 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.