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Geometry and Global Stability of 2D Periodic Monotone Maps

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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.

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Acknowledgements

This work was partially supported by FCT/Portugal through the project UIDB/04459/2020. We also thank the anonymous referee for their insightful suggestions to improve this article.

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Authors and Affiliations

  1. Department of Mathematics, Trinity University, San Antonio, TX, USA

    E. Cabral Balreira

  2. Center for Mathematical Analysis, Geometry, and Dynamical Systems, Instituto Superior Tecnico, Technical University of Lisbon, Lisbon, Portugal

    Rafael Luís

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  1. E. Cabral Balreira
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  2. Rafael Luís
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Correspondence to E. Cabral Balreira.

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Balreira, E.C., Luís, R. Geometry and Global Stability of 2D Periodic Monotone Maps. J Dyn Diff Equat 35, 2185–2198 (2023). https://doi.org/10.1007/s10884-021-10089-z

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  • DOI: https://doi.org/10.1007/s10884-021-10089-z

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