A PREDATOR-PREY MODEL WITH ALLEE EFFECT AND FAST STRATEGY EVOLUTION DYNAMICS OF PREDATORS USING HAWK AND DOVE TACTICS

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Authors

KÜHNOVÁ Jitka PŘIBYLOVÁ Lenka

Year of publication 2011
Type Article in Periodical
Magazine / Source APPLIED MATHEMATICS AND INFORMATICS
MU Faculty or unit

Faculty of Science

Citation
Web http://www.sav.sk/journals/uploads/0127102402ku-pr.pdf
Doi http://dx.doi.org/10.2478/v10127-011-0033-1
Field General mathematics
Keywords prey predator model; Allee effect; strategy evolution; bifurcation; Hawk Dove evolution
Description 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 Sanchez (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 find 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.
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