An Investigation of Additional Food Models with Generalised Functional Response

Abstract

Additional food sources are often used to improve the effectiveness of predators in controlling pest populations. However, the non-symmetric structure of additional food predator-prey models can cause certain aspects of their dynamics challenging to analyze. In this work, we study a general class of additional food models and establish conditions under which the coexistence equilibrium is globally stable. We then focus on a Holling type IV functional response with AF and show the existence of a Bogdanov-Takens bifurcation of codimension 3. We also study these models through the lens of deterministic chemical reaction network theory. Our analysis shows that the introduction of additional food increases the deficiency of the underlying reaction network and suggests a possible link between higher deficiency and complex bifurcations.