Periodicity in a ratio-dependent predator–prey system with stage-structured predator on time scales

Abstract

This paper investigates the existence of periodic solutions of a ratio-dependent predator–prey system with stage-structured predator on time scales. We obtain criteria for the existence of periodic solutions of such a 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. The main approach is based on Gaines and Mawhin's continuation theorem of coincidence degree theory. This approach has been extensively used in studying existence problems in differential equations and difference equations, while it is rarely applied to study equations on time scales.