Abstract
In this paper, a delayed prey–predator model with discontinuous harvesting policies is investigated, in which the predator population consumes the prey according to Hassell–Varley-type functional response. Under some reasonable assumptions on the discontinuous harvesting functions, the local existence and global existence of positive solution in sense of Filippov to the system are obtained. Based on the functional differential inclusions theory and the topological degree theory of set-valued analysis, a series of useful criteria on existence and non-existence of the positive periodic solution is established for the system. Finally, some numerical examples are given to show the applicability and effectiveness of the obtained results. It is worthy to point out that the discontinuous harvesting policies are superior to continuous harvesting policies, which are usually adopted in previous papers.
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