Periodic solutions for a delayed predator–prey system with stage-structured predator on time scales

In this paper, a modified delayed predator–prey system with stage structure for predator is proposed and studied, which generalizes and incorporates as special cases some known models. With the help of continuation theorem based on the Gaines and Mawhin coincidence degree theory, we investigate the existence of periodic solutions for the proposed delayed predator–prey system with stage-structured predator and two kinds of functional responses (called Holling III functional response and Beddington–DeAngelis functional response) on time scales. In particular, when the time scale is chosen as the set of the real numbers or the integers, the existence of the periodic solutions of the corresponding continuous-time and discrete-time models follows.