Local stability conditions for a n-dimensional periodic mapping

Rafael Luís and Sandra Mendonça

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 218, issue C, 15-30

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.

Keywords: Periodic difference equations; Asymptotic stability; Periodic solutions; Applications (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:218:y:2024:i:c:p:15-30

DOI: 10.1016/j.matcom.2023.11.023

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