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Local Stability in 3D Discrete Dynamical Systems: Application to a Ricker Competition Model

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  • Rafael Luís
  • Elias Rodrigues

Abstract

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.

Suggested Citation

  • Rafael Luís & Elias Rodrigues, 2017. "Local Stability in 3D Discrete Dynamical Systems: Application to a Ricker Competition Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-16, July.
    • Handle: RePEc:hin:jnddns:6186354
    DOI: 10.1155/2017/6186354
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    Cited by:

    1. Matvey Kulakov & Galina Neverova & Efim Frisman, 2022. "The Ricker Competition Model of Two Species: Dynamic Modes and Phase Multistability," Mathematics, MDPI, vol. 10(7), pages 1-23, March.

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