| This paper consists of three parts:Firstly,we investigate the effect of impulsive stocking on the species that live in a weakly ecological environment.Different from the former studies,we pay attention to the more important situation in conservation biology in which species have the negative growth,which means that the species will be extinct without the interference of the human being.We obtain an interesting result:the species can persist for rational stocking,and if we further assume that the stocking is periodic,the system admits unique periodic positive solution,and the system might also be driven to extinction if the stocking of the species is too small.Secondly,we propose and study an impulsive competition model with Beddington-DeAngelis functional response and the effect of toxic substances.Sufficient conditions which ensure the permanence and extinction of the partial species are obtained,respectively,by applying the comparison theorem of the impulsive differential equation and constructing a suitable Lyapunov type extinction function.Our results show that the inferior competitor and the other competitor can coexist in a stable state under the appropriate impulsive stocking.Numerical simulations support our findings.Thirdly,the dynamic behavior of a Logistic model incorporate of nonlinear impulsive harvesting is proposed and studied.Here,we use the Holling ? functional response to describe the harvesting procedure.Sufficient conditions for both permanence and extinction of the system are established,respectively,by using techniques derived from the theory of impulsive differential equations.Out study shows that the impulsive controls play an important role in maintaining the sustainable development of the ecological.Compared with the linear impulsive capture or nonlinear capture,our study shows that the nonlinear impulsive capture could lead to more complicated dynamic behaviors.Our results give some useful information to the practical biological economics management. |
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