Existence of periodic solutions for a predator–prey system with sparse effect and functional response on time scales

In this paper, we systematically investigates the existence of periodic solutions of a predator–prey system with sparse effect and Beddington–DeAngelis or Holling III functional response on time scales. By using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of periodic solutions for the systems. Moreover, when the time scale TT is chosen as RR or ZZ, 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 paper discusses predator–prey systems with sparse effect and functional response on time scales.
► Some existence results are obtained and the studies of differential and difference equations are unified.
► These results can be extended to more general time scales.