RESUMEN
In this paper, a stochastic hybrid delay food chain model with jumps in an impulsive polluted environment is investigated. We obtain the sufficient and necessary conditions for persistence in mean and extinction of each species. The results show that the stochastic dynamics of the system are closely correlated with both time delays and environmental noises. Some numerical examples are introduced to illustrate the main results.
RESUMEN
This paper concerns the dynamics of two stochastic hybrid delay Lotka-Volterra systems with harvesting and Lévy noise in a polluted environment (i.e., predator-prey system and competitive system). For every system, sufficient and necessary conditions for persistence in mean and extinction of each species are established. Then, sufficient conditions for global attractivity of the systems are obtained. Finally, sufficient and necessary conditions for the existence of optimal harvesting strategy are provided. The accurate expressions for the optimal harvesting effort (OHE) and the maximum of expectation of sustainable yield (MESY) are given. Our results show that the dynamic behaviors and optimal harvesting strategy are closely correlated with both time delays and three types of environmental noises (namely white Gaussian noises, telephone noises and Lévy noises).