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<p>In this study, we derive and analyze an additional food provided prey-predator model with Holling type-III functional response, incorporating mutual interference among predators. Despite extensive research on biological pest control, a significant scientific gap remains in understanding how mutual interference and slow predation dynamics interact with external food supplementation strategies under optimal control frameworks. Our work addresses this gap by investigating the impact of additional food and competition on pest dynamics and predator efficiency. Preliminary results establish the positivity and boundedness of the model solutions. We demonstrate the existence of equilibria, their local stability and bifurcation analysis. Global dynamics and system stability are explored with respect to key parameters using numerical simulations. Furthermore, we frame and characterize the time optimal control problems-considering the quality and quantity of additional food as control variables-using Pontryagin’s maximum principle and numerical optimization techniques. Our findings reveal that strategic food provisioning can drive the system toward prey elimination, contributing to a pest-regulated ecosystem. This study offers a novel perspective by integrating ecological interactions, control theory and sustainable pest management strategies.</p>

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Global dynamics and time-optimal control studies for additional food provided holling type-III mutually interfering prey-predator systems with applications to pest management

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  • 出版模式：

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  • 发表日期：

    2025年8月2日

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  • D. Bhanu Prakash,
  • D. K. K. Vamsi

摘要

In this study, we derive and analyze an additional food provided prey-predator model with Holling type-III functional response, incorporating mutual interference among predators. Despite extensive research on biological pest control, a significant scientific gap remains in understanding how mutual interference and slow predation dynamics interact with external food supplementation strategies under optimal control frameworks. Our work addresses this gap by investigating the impact of additional food and competition on pest dynamics and predator efficiency. Preliminary results establish the positivity and boundedness of the model solutions. We demonstrate the existence of equilibria, their local stability and bifurcation analysis. Global dynamics and system stability are explored with respect to key parameters using numerical simulations. Furthermore, we frame and characterize the time optimal control problems-considering the quality and quantity of additional food as control variables-using Pontryagin’s maximum principle and numerical optimization techniques. Our findings reveal that strategic food provisioning can drive the system toward prey elimination, contributing to a pest-regulated ecosystem. This study offers a novel perspective by integrating ecological interactions, control theory and sustainable pest management strategies.