| Abstract: |
| The literature posits that an introduced predator population is able to drive its target pest population to extinction, if supplemented with high quality additional food of sufficient quantity. We show this approach actually leads to infinite time blow-up of the predator population, so is unpragmatic as a pest management strategy. We propose an alternate model in which the additional food induces predator competition. Analysis of this model indicates that depending on the competition parameter $c$, one can have global stability of the pest free state, bi-stability dynamics, or up to three interior equilibria. As $c$ and the additional food quantity $\xi$ are varied standard co-dimension one and co-dimension two bifurcations are observed. We also use structural symmetries to construct several non-standard bifurcations such as saddle-node-transcritical bifurcation (SNTC) in co-dimension two and a cusp-transcritical bifurcation (CPTC), also in co-dimension two. We further use symmetry to construct a novel pitchfork-transcritical bifurcation (PTC) in co-dimension two, thus explicitly characterizing a new organizing center of the model. Our findings indicate that increasing additional food in predator-pest models can hinder bio-control, contrarily to some of the literature. However, additional food that also induces predator competition, leads to rich dynamics and enhances bio-control. |
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