AI Insight
This mathematical study examines predator-prey models that incorporate additional food sources for predators, which are commonly used in biological pest control strategies. The researchers establish mathematical conditions for stable coexistence between predators and prey, and identify complex bifurcation behavior (specifically a codimension 3 Bogdanov-Takens bifurcation) when using a Holling type IV functional response model. The analysis using chemical reaction network theory reveals that adding supplemental food increases network deficiency, potentially correlating with more complex system dynamics.
Why it matters
The findings provide theoretical foundations for optimizing biological pest control programs that use supplemental feeding of predator populations. Understanding the stability conditions and potential for complex dynamics helps predict when additional food strategies will effectively control pests versus when they might lead to unpredictable population fluctuations.
Understand the Science
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.
Source: An Investigation of Additional Food Models with Generalised Functional Response