Local stability in 3D discrete dynamical systems: application to a Ricker competition model

Luís, Rafael; Rodrigues, Elias

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http://hdl.handle.net/10400.13/4105

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Authors

Luís, Rafael

Rodrigues, Elias

Abstract(s)

A survey on the conditions of local stability of fixed points of three-dimensional discrete dynamical systems or difference equations is provided. In particular, the techniques for studying the stability of nonhyperbolic fixed points via the centre manifold theorem are presented. A nonlinear model in population dynamics is studied, namely, the Ricker competition model of three species. In addition, a conjecture about the global stability of the nontrivial fixed points of the Ricker competition model is presented.

Keywords

Local stability Local stability in 3D Discrete dynamical system Ricker competition model . Faculdade de Ciências Exatas e da Engenharia

URI

http://hdl.handle.net/10400.13/4105

Citation

Luís, R., & Rodrigues, E. (2017). Local stability in 3D discrete dynamical systems: application to a Ricker competition model. Discrete Dynamics in Nature and Society, 2017. https://doi.org/10.1155/2017/6186354