Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 243974, 12 pages
doi:10.1155/2009/243974

Double periodic solutions for a ratio-dependent predator-prey system with harvesting terms on time scales

Abstract

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 ℝ or ℤ, 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.