Abstract: | This paper investigates the existence of periodic solutions of a three-species food-chain diffusive system with Beddington-DeAngelis
functional responses and time delays in a two-patch environment 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 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 method
is unified to provide the existence of the desired solutions for continuous differential equations and discrete difference
equations. |