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Periodic monotone systems having one-dimensional dynamics

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Abstract

We establish a criterion for a periodic monotone system to display a fully one dimensional dynamical behavior. This criterion is based on the existence of a Lyapunov function acting on differences of unordered solutions. The main consequence is the convergence of every solution to a periodic one.

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  1. Departamento de Matemática Aplicada y Estadística, Escuela Universitaria de Ingeniería Técnica Civil, Universidad Politécnica de Cartagena, 30203, Cartagena (Murcia), Spain

    Luis A. Sanchez

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  1. Luis A. Sanchez
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Correspondence to Luis A. Sanchez.

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Supported by MTM2008-02502.

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Sanchez, L.A. Periodic monotone systems having one-dimensional dynamics. Arch. Math. 94, 235–243 (2010). https://doi.org/10.1007/s00013-009-0090-8

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  • DOI: https://doi.org/10.1007/s00013-009-0090-8

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