A predator-prey model with allee effect and fast strategy evolution dynamics of predators using hawk and dove tactics

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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 S´anchez (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.

[1] AUGER, P.-PARRA, R. B-MORAND, S.-SÁNCHEZ, E.: A predator-prey model with predators using hawk and dove tactics, Mathematical Biosciences 177&178 (2002), 185-200.

[2] KUZNETSOV, Y. A.: Elements of Applied Bifurcation Theory. Springer-Verlag, Berlin, New York, Inc. 1998.

Tatra Mountains Mathematical Publications

The Journal of Slovak Academy of Sciences

Journal Information


CiteScore 2017: 0.37

SCImago Journal Rank (SJR) 2017: 0.363
Source Normalized Impact per Paper (SNIP) 2017: 0.482

Mathematical Citation Quotient (MCQ) 2017: 0.14

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researchers in the all fields of mathematical research

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