Time-Optimal Control Studies for Additional Food provided Prey-Predator Systems involving Holling Type-III and Holling Type-IV Functional Responses

TL;DR

This paper investigates time-optimal control strategies for prey-predator systems with Holling type-III and IV functional responses, focusing on optimizing additional food provision to enhance pest management effectiveness.

Contribution

It introduces a mathematical framework for optimal control of prey-predator models with Holling responses, including existence, uniqueness, and Pontryagin maximum principle-based characterization.

Findings

Optimal quality and quantity of additional food are characterized.

The models demonstrate potential applications in pest management.

Existence and uniqueness of solutions are established.

Abstract

In recent years, time-optimal control studies on additional food provided prey-predator systems have gained significant attention from researchers in the field of mathematical biology. In this study, we initially consider an additional food provided prey-predator model exhibiting Holling type-III functional response and the intra-specific competition among predators. We prove the existence and uniqueness of global positive solutions for the proposed model. We do the time optimal control studies with respect quality and quantity of additional food as control variables by transforming the independent variable in the control system. Making use of the Pontraygin maximum principle, we characterize the optimal quality of additional food and optimal quantity of additional food. We show that the findings of these time-optimal control studies on additional food provided prey-predator systems involving Holling type III functional response have the potential to be applied to a variety of problems in pest management. In the later half of this study, we consider an additional food provided prey-predator model exhibiting Holling type-IV functional response and study the above aspects for this system.