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Local stability conditions for a n-dimensional periodic mapping

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  • Luís, Rafael
  • Mendonça, Sandra

Abstract

In this paper we determine the necessary and sufficient conditions for asymptotically stability of periodic cycles for periodic difference equations by using the Jury’s conditions. Such conditions are obtained using the information of the Jacobian matrices of the individual maps, avoiding thus the computation of the Jacobian matrix of the composition operator, which in higher dimension can be an a very difficult task. We illustrate our ideas by using models in population dynamics and in economics game theory.

Suggested Citation

  • Luís, Rafael & Mendonça, Sandra, 2024. "Local stability conditions for a n-dimensional periodic mapping," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 15-30.
    • Handle: RePEc:eee:matcom:v:218:y:2024:i:c:p:15-30
    DOI: 10.1016/j.matcom.2023.11.023
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    References listed on IDEAS

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    1. Richard William Farebrother, 2012. "Sufficient Conditions For The Stability Of Linear Difference Equations," Manchester School, University of Manchester, vol. 80(5), pages 630-632, September.
    2. Bischi, Gian-Italo & Stefanini, Luciano & Gardini, Laura, 1998. "Synchronization, intermittency and critical curves in a duopoly game," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 44(6), pages 559-585.
    3. Marji Lines & Noemi Schmitt & Frank Westerhoff, 2020. "Stability conditions for three-dimensional maps and their associated bifurcation types," Applied Economics Letters, Taylor & Francis Journals, vol. 27(13), pages 1056-1060, June.
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