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NECESSARY AND SUFFICIENT CONDITION FOR THE PERIODIC SOLUTIONS OF PREDATOR-PREY DYNAMIC SYSTEMS WITH BEDDINGTON-DEANGELIS TYPE FUNCTIONAL RESPONSE

We consider two dimensional predator-prey system with Beddington-DeAngelis type functional response on time scales. For this special case we try to find the necessary and sufficient conditions for the considered system when it has at least one w-periodic solution. This study is mainly based on continuation theorem in coincidence degree theory and will also give beneficial results for continuous and discrete case. Especially, for the continuous case, by using the study of [7], to obtain the globally attractive w-periodic solution of the given system, an inequality is given as the necessary and sufficient condition.