Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 243974, 12 pages
Research Article

Double Periodic Solutions for a Ratio-Dependent Predator-Prey System with Harvesting Terms on Time Scales

School of Mathematics and Computer, Harbin University, Harbin, Heilongjiang 150086, China

Received 6 April 2009; Accepted 1 September 2009

Academic Editor: Guang Zhang

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.


We investigate a nonautonomous ratio-dependent predator-prey model with Beddington-DeAngelis functional response and multiple harvesting (or exploited) terms on time scales. By means of using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of at least two periodic solutions for the system. Moreover, when the time scale 𝕋 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.