Title

Geometry and Global Stability of 2D Periodic Monotone Maps

Document Type

Article

Publication Date

10-7-2021

Abstract

We establish conditions to ensure global stability of a competitive periodic system from hypotheses on individual maps. We study planar competitive maps of Kolgomorov type. We show how conditions for global stability for individual maps will remain invariant under composition and hence establish a globally stable cycle. Our main theoretical contribution is to show that stability for monotone non-autonomous periodic maps can be reduced to a problem of global injectivity. We provide analytic conditions that can be checked and illustrate our results with important competition models such as the planar Leslie-Gower and Ricker maps.

DOI

10.1007/s10884-021-10089-z

Publisher

Springer Nature

Publication Information

Journal of Dynamics and Differential Equations

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