Abstract
In this study, a class of delayed prey–predator model with Hassell–Varley type functional response is investigated, in which the harvesting policies are modeled by discontinuous functions. Based on functional differential inclusions and set-valued analysis theories, the local and global existence of positive solution in sense of Filippov is given. By employing theory of functional differential inclusions and generalized differential inequalities, some sufficient conditions which guarantee the permanence of the system are obtained. According to non-smooth analysis theory with generalized Lyapunov functional approach, a series of useful criteria on existence, uniqueness and global asymptotic stability of the almost positive periodic solution to the system are derived. Some suitable examples together with their numerical simulations are given to illustrate the effectiveness of our results by using MATLAB.
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