On hybrid stochastic population models with impulsive perturbations

Abstract

This paper considers the dynamic behaviours of a hybrid stochastic population model with impulsive perturbations. The existence of the global positive solution is studied in this paper. Moreover, under some conditions on the noises and impulsive perturbations, the properties of the persistence and extinction, stochastic permanence, global attractivity and stability in distribution are presented. Our results illustrate that impulsive perturbations play a crucial role in these properties. The bounded impulse term will not affect these properties, however, when the impulse term is unbounded, some of the properties, such as the persistence and extinction may be changed significantly. As a part of this paper, a couple of examples and numerical simulations are provided to illustrate our results.

Mathematical and numerical analyses of a stochastic impulse control model with imperfect interventions

“…Impulse control models have been applied to various problems, such as predator-prey population management [25], fishery resources management [26], aquaculture operation [27], tree harvesting [28,29], and waterbird management [30]. Deep mathematical analysis of the impulse control models of population dynamics and related models have been carried out [31,32]. Other important industrial problems, such as gene regulation [33] and satellite control [34,35], have been considered with the impulse control as well.…”