In this paper, on the basis of the theories and methods of ecology and ordinary differential equations, a three-species ecological model with allochthonous nutrient input, impulse perturbations and seasonal disturbances is studied analytically and numerically. Using mathematical theoretical...

In this work, according to integrated pest management principles, a class of predator–prey system with state-dependent impulsive effects is put forward. In this model, the control strategies by releasing natural enemies and spraying pesticide at different thresholds are considered. The...

In this paper, the continuous and impulsive harvesting policies are considered in a predator–prey system with stage-structure. In the case in which a continuous harvesting is used, it is shown that the mature predator becomes extinct under appropriate conditions. In the case in which an...

In this work, we propose a delayed predator–prey model with impulsively diffusive prey between two patches. Using the stroboscopic map of the discrete dynamical system, we obtain the globally attractive condition of predator-extinction periodic solution of the system. We also obtain the...

In this paper, an SEIR epidemic disease model with time delay and nonlinear incidence rate is studied, and the dynamical behavior of the model under pulse vaccination is analyzed. Using the discrete dynamical system determined by the stroboscopic map, we show that there exists an infection-free...

Based on biological control strategy in pest management, we construct and investigate a pest-epidemic model with impulsive control, i.e., periodic spraying microbial pesticide and releasing infected pests at different fixed moments. By using Floquet theorem and comparison theorem, we prove that...

In this paper, we investigate the extinction, permanence and dynamic complexity of the two-prey, one-predator system with Ivlev's functional response and impulsive perturbation on the predator at fixed moments. Conditions for the extinction and permanence of the system are established via the...

In this work, we consider a stage-structured pest management SI model with time delay and diseased pests impulsive transmission. Sufficient conditions which guarantee the global attractivity of pest-extinction periodic solution and permanence of the system are obtained. We also prove that all...

We establish a discrete time non-autonomous two-species mutualistic system with delays by considering the influence of many generations on the density of species population. With the help of the method of coincidence degree and some techniques, an easily verifiable sufficient condition is...

We investigate a three-species food chain system with density-dependent birth rate and impulsive effect concerning biological and chemical control strategy — periodic releasing of natural enemies or spraying pesticide at different fixed times. Conditions for the extinction of the prey and top...