Global Dynamics and Time-Optimal Control Studies for Additional Food provided Holling Type-III Mutually Interfering Prey-Predator Systems with Applications to Pest Management

TL;DR

This paper models prey-predator dynamics with Holling type-III response and predator interference, analyzing how additional food provision can control pests and achieve prey elimination through optimal control strategies.

Contribution

It introduces a mathematical framework for understanding the effects of additional food on predator-prey systems with mutual interference, including stability analysis and optimal control applications.

Findings

Provision of suitable additional food leads to prey elimination.

System stability is influenced by the quality and quantity of added food.

Optimal control strategies can effectively manage pest populations.

Abstract

In this study, we investigate a prey-predator model exhibiting Holling type-III functional response among mutually interfering predators to assess the effects of provision of additional food to natural enemies in altering pest dynamics. We derive and study both the non-additional food provided system (initial system) and additional food provided system mathematically and through extensive numerical simulations. We prove the positivity and boundedness of the solutions of both the systems. We perform an extensive existence and stability analysis of various equilibrium points exhibited by both the systems. We discuss the global dynamics and stability behavior exhibited by both the systems with respect to crucial parameters using numerical methods. Considering the quality and quantity of additional food as control parameters, we framed and characterized the time optimal control problems. We further simulated these time optimal problems using numerical optimization techniques. Our theoretical and numerical investigations reveal that the provision of suitable choice of additional food steers the system to a prey-elimination state, leading to a pest-regulated ecosystems.