Dynamical Analysis of Additional Food Models with Mutual Interaction in Predator-Prey Systems for Pest Control

SureniWickramasooriya

Univeresity of California - Davis

"Dynamical Analysis of Additional Food Models with Mutual Interaction in Predator-Prey Systems for Pest Control"

The supplementation of additional food (AF) to introduced predators has been explored as a strategy to enhance pest control. However, AF models with prey-dependent functional responses can lead to unbounded predator growth. To address this, an AF model incorporating mutual interference has been proposed, demonstrating that pest eradication is feasible when the AF quantity ξξ exceeds a threshold function of the interference parameter ϵϵ. In this study, we revisit and extend this model, uncovering novel dynamical behaviors. We show that pest eradication occurs within a narrower AF range and can be bi-stable or globally attracting, arising through a saddle-node bifurcation. Additionally, we identify Hopf and global homoclinic bifurcations, revealing a unique dynamic where the pest extinction state becomes an 'almost' global attractor. This is the first analytical proof of such a structure in AF models, providing insights into bio-control strategies under varying predator interference conditions.
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