Local stability conditions for a n-dimensional periodic mapping

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.

Automated summary

This paper determines the necessary and sufficient conditions for the asymptotic stability of periodic cycles for periodic difference equations using Jury's conditions. The conditions are obtained using the Jacobian matrices of the individual maps, avoiding the computation of the Jacobian matrix of the composition operator, which can be a challenging task in higher dimensions. The ideas are illustrated using models in population dynamics and economics game theory.