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Title of Journal: Nonlinear Dyn

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Abbravation: Nonlinear Dynamics

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Springer Netherlands

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DOI

10.1002/cjoc.200591120

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1573-269X

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Stochastic optimal control of predator–prey ecosys

Authors: X D Gu W Q Zhu
Publish Date: 2016/04/01
Volume: 85, Issue: 2, Pages: 1177-1184
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Abstract

A new control strategy for preventing the extinction of predator–prey ecosystem in a random environment is proposed First a controlled stochastic Lotka–Volterra system is introduced and its some properties are presented The stochastic averaging method is applied to transfer the original controlled system to a partially averaged one Then the adjoint equation and maximum condition of the partially averaged control problem are derived based on the stochastic maximum principle The optimal control is determined from the maximum condition and solving the forwardbackward stochastic differential equation FBSDE For infinite timeinterval ergodic control the adjoint process is stationary and the FBSDE is reduced to an ordinary differential equation Finally the stationary probability density of the prey of optimally controlled system is obtained to show that the controlled ecosystem is more stable than the uncontrolled one The mean transition time of optimally controlled system is also calculated to show that the proposed control strategy is effective in preventing the possible extinction

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