Analysis of a Single Species Model with Dissymmetric Bidirectional Impulsive Diffusion and Dispersal Delay

In most models of population dynamics, diffusion between two patches is assumed to be either continuous or discrete, but in the real natural ecosystem, impulsive diffusion provides a more suitable manner to model the actual dispersal (or migration) behavior for many ecological species. In addition, the species not only requires some time to disperse or migrate among the patches but also has some possibility of loss during dispersal. In view of these facts, a single species model with dissymmetric bidirectional impulsive diffusion and dispersal delay is formulated. Criteria on the permanence and extinction of species are established. Furthermore, the realistic conditions for the existence, uniqueness, and the global stability of the positive periodic solution are obtained. Finally, numerical simulations and discussion are presented to illustrate our theoretical results

Existence and stability of periodic solution of a Lotka–Volterra predator–prey model with state dependent impulsive effects

AbstractAccording to biological and chemical control strategy for pest, we investigate the dynamic behavior of a Lotka–Volterra predator–prey state-dependent impulsive system by releasing natural enemies and spraying pesticide at different thresholds. By using Poincaré map and the properties of the Lambert W function, we prove that the sufficient conditions for the existence and stability of semi-trivial solution and positive periodic solution. Numerical simulations are carried out to illustrate the feasibility of our main results