Stochastic dynamics of a hybrid delay food chain model with harvesting and jumps in an impulsive polluted environment

Abstract

In this paper, we propose a stochastic hybrid delay food chain model with harvesting (under
catch-per-unit-effort hypothesis) and jumps in an impulsive polluted environment. First, we study some
stochastic dynamic properties of the system by stochastic analysis techniques, such as persistence in mean,
extinction and global attractivity of the system. Then, we research the optimal harvesting problem of the
system by ergodic theory. The accurate expressions for the optimal harvesting effort (OHE, for short) and
the maximum of expectation of sustainable yield (MESY, for short) are given. Our results show that the
stochastic dynamics and optimal harvesting strategy (OHS, for short) of the system are closely correlated
with both time delays and environmental noises. Finally, some numerical simulations are introduced to
illustrate the main results.