Stochastic Optimal and Time-Optimal Control Studies for Additional Food provided prey-predator Systems involving Holling Type-III Functional Response

TL;DR

This paper presents a stochastic optimal control analysis of a prey-predator model with Holling Type-III response, focusing on biological conservation and pest management, using numerical simulations to validate the theoretical results.

Contribution

It introduces a novel stochastic optimal control framework for prey-predator systems with additional food and Holling Type-III response, including time-optimal control analysis.

Findings

Existence of optimal controls established via stochastic maximum principle

Numerical simulations demonstrate effective control strategies

Results applicable to conservation and pest management

Abstract

This paper consists of a detailed and novel stochastic optimal control analysis of a coupled non-linear dynamical system. The state equations are modeled as additional food provided prey-predator system with Holling Type-III functional response for predator and intra-specific competition among predators. We firstly discuss the optimal control problem as a Lagrangian problem with a linear quadratic control. Secondly we consider an optimal control problem in the time-optimal control setting. Stochastic maximum principle is used for establishing the existence of optimal controls for both these problems. Numerical simulations are performed based on stochastic forward-backward sweep methods for realizing the theoretical findings. The results obtained in these optimal control problems are discussed in the context of biological conservation and pest management.