A predator{prey model with Allee effect and fast strategy evolution dynamics of predators using Hawk and Dove tactics

Abstract

In this work we present the predator{prey model with Allee effect and Hawk and Dove
tactics in fighting over caught prey implemented as fast strategy evolution dynamics. We
extend the work of Auger, Parra, Morand and Sánchez (2002) using the prey population
embodying Allee effect and analogously to this work we get two connected submodels with
polymorphic and monomorphic predator population. We get much richer dynamics, in
each submodel we nd local bifurcations (saddle-node, supercritical Hopf caused by Allee
effect and Bogdanov{Takens) and a global bifurcation of limit cycles caused by the strategy
evolution that is not possible in any of the submodels that can lead to a bluesky extinction
of both populations.