Abstract
We consider a delayed Holling type II predator-prey system with birth pulse and impulsive harvesting on predator population at different moments. Firstly, we prove that all solutions of the investigated system are uniformly ultimately bounded. Secondly, the conditions of the globally attractive prey-extinction boundary periodic solution of the investigated system are obtained. Finally, the permanence of the investigated system is also obtained. Our results provide reliable tactic basis for the practical biological economics management.
Highlights
Theories of impulsive differential equations have been introduced into population dynamics lately 1, 2
An impulsive differential equation to model the process of releasing infective pests and spraying pesticides at different fixed moment was represented as dS t dt dI t dt rS t
We suggest impulsive differential equations to model the process of periodic birth pulse and impulsive harvesting
Summary
Theories of impulsive differential equations have been introduced into population dynamics lately 1, 2. In most models of population dynamics, increase in population due to birth are assumed to be time dependent, but many species reproduce only during a period of the year. We suggest impulsive differential equations to model the process of periodic birth pulse and impulsive harvesting. X t βy t − rx t − βe−rτ y t − τ , 1.6 y t βe−rτ y t − τ − η2y2 t , where x t , y t represent the immature and mature populations densities, respectively, τ represents a constant time to maturity, and β, r and η2 are positive constants We consider a delayed Holling type II predatorprey system with birth pulse and impulsive harvesting on predator population at different moments.
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