Stochastic Time-Optimal Control Studies for Additional Food provided Prey-Predator Systems involving Holling Type-IV Functional Response

TL;DR

This paper models prey-predator dynamics with Holling type IV response under stochastic noise, establishing conditions for optimal additional food provision to enhance biological conservation and pest control.

Contribution

It introduces a stochastic prey-predator model with control parameters for additional food, deriving conditions for optimal food quality and quantity using stochastic maximum principle.

Findings

Existence and uniqueness of global positive solutions.

Characterization of optimal food parameters via stochastic maximum principle.

Numerical illustrations demonstrating practical applications.

Abstract

We consider an additional food provided prey-predator model exhibiting Holling type IV functional response with combined continuous white noise and discontinuous L\'evy noise. We prove the existence and uniqueness of global positive solutions for the considered model. By considering the quality and quantity of additional food as control parameters, we formulate a time-optimal control problem. We obtain the condition for the existence of an optimal control. Furthermore, making use of the arrow condition of the sufficient stochastic maximum principle, we characterize the optimal quality of additional food and optimal quantity of additional food. Numerical results are given to illustrate the theoretical findings with applications in biological conservation and pest management.