Dynamical analysis of a logistic model with impulsive Holling type-II harvesting. (English) Zbl 1445.92242
Summary: A logistic model with impulsive Holling type-II harvesting is proposed and investigated in this paper. Here, the species is harvested at fixed moments. By using the techniques derived from the theory of impulsive differential equations, sufficient conditions for both permanence and extinction of the system are established, respectively. Sufficient conditions which ensure the existence, uniqueness, and global attractivity of a positive periodic solution of the system are obtained. Our study shows that impulsive controls play an important role in maintaining the sustainable development of the ecological system. Compared with the linear impulsive capture or continuous nonlinear-type capture, our study shows that the nonlinear impulsive capture could lead to more complicated dynamic behaviors. Numeric simulations are carried out to show the feasibility of the main results. The results obtained here maybe useful to the practical biological economics management.
MSC:
| 92D25 | Population dynamics (general) |
| 34C25 | Periodic solutions to ordinary differential equations |
| 34D20 | Stability of solutions to ordinary differential equations |
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