Dynamics and response reshaping of nonlinear predator-prey system undergoing random abrupt disturbances

Abstract

An actual ecological predator-prey system often undergoes random environmental mutations owing to the impact of natural disasters and man-made destruction, which may destroy the balance between the species. In this paper, the stochastic dynamics of the nonlinear predator-prey system considering random environmental mutations is investigated, and a feedback control strategy is proposed to reshape the response of the predator-prey system against random abrupt environmental mutations. A delayed Markov jump system (MJS) is established to model such a predator-prey system. A novel first integral is constructed which leads to better approximation solutions of the ecosystem. Then, by applying the stochastic averaging method based on this novel first integral, the stochastic response of the predator-prey system is investigated, and an analytical feedback control is designed to reshape the response of the ecosystem from the disturbed state back to the undisturbed one. Numerical simulations finally illustrate the accuracy and effectiveness of the proposed procedure.