Dynamical analysis and optimal control in a hybrid stochastic double delayed bioeconomic system with impulsive contaminants emission and Lévy jumps.

Highlights • A hybrid stochastic double delayed system with impulse and Lévy jumps is proposed. • Combined dynamic effects of impulse, time delays and Lévy jumps are investigated. • Sufficient conditions for persistence in the mean and extinction are investigated. • The asymptotical stability in distribution of the proposed hybrid system is studied. • Optimal price control and maximum of expectation of sustainable yield are discussed. Abstract In this paper, a hybrid stochastic double delayed prey predator bioeconomic system with impulses and Lévy jumps is established, where commercial harvesting on each population and impulsive contaminants emission from surrounding environment on each population growth are taken into account. Sufficient conditions for persistence in the mean and extinction of interacting population are investigated. The asymptotical stability in distribution of the proposed system is studied. Furthermore, optimal price control strategy and maximum of expectation of sustainable yield are discussed. Numerical simulations are carried out to illustrate theoretical analysis. [ABSTRACT FROM AUTHOR]