<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

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

Faculty of Science, University of Hradec Králové, Rokitanského 62, CZ–500-03 Hradec Králové, CZECH REPUBLIC

Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, CZ–611-37 Brno, CZECH REPUBLIC

Tatra Mountains Mathematical Publications

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...

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

Published Online: Nov 13, 2012

Page range: 13 - 24

DOI: https://doi.org/10.2478/v10127-011-0033-1

Keywords
prey-predator model, Allee effect, strategy evolution, bifurcation, Hawk-Dove evolution.

This content is open access.

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

Published Online: Nov 13, 2012

Page range: 13 - 24

DOI: https://doi.org/10.2478/v10127-011-0033-1

Keywordsprey-predator model, Allee effect, strategy evolution, bifurcation, Hawk-Dove evolution.

This content is open access.

Keywords
prey-predator model, Allee effect, strategy evolution, bifurcation, Hawk-Dove evolution.