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Nonautonomous Dynamical Systems in the Life Sciences

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Nonautonomous Dynamical Systems in the Life Sciences

Part of the book series: Lecture Notes in Mathematics ((LNMBIOS,volume 2102))

Abstract

Nonautonomous dynamics describes the qualitative behavior of evolutionary differential and difference equations, whose right-hand side is explicitly time-dependent. Over recent years, the theory of such systems has developed into a highly active field related to, yet recognizably distinct from that of classical autonomous dynamical systems. This development was motivated by problems of applied mathematics, in particular in the life sciences where genuinely nonautonomous systems abound. In this survey, we introduce basic concepts and tools for appropriate nonautonomous dynamical systems and apply them to various representative biological models.

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Acknowledgements

Peter E. Kloeden was partially supported by the DFG grant KL 1203/7-1, the Spanish Ministerio de Ciencia e Innovación project MTM2011-22411, the Consejería de Innovación, Ciencia y Empresa (Junta de Andalucía) under the Ayuda 2009/FQM314 and the Proyecto de Excelencia P07-FQM-02468.

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  1. Institut für Mathematik, Goethe-Universität Frankfurt, 11 19 32, 60054, Frankfurt am Main, Deutschland

    Peter E. Kloeden

  2. Institut für Mathematik, Alpen-Adria Universität Klagenfurt, Universitätsstraße 65–67, 9020, Klagenfurt am Wörthersee, Österreich

    Christian Pötzsche

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  1. Institut für Mathematik, Goethe-Universität Frankfurt, Frankfurt am Main, Germany

    Peter E. Kloeden

  2. Institut für Mathematik, Alpen-Adria Universität Klagenfurt, Klagenfurt am Wörthersee, Austria

    Christian Pötzsche

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Kloeden, P.E., Pötzsche, C. (2013). Nonautonomous Dynamical Systems in the Life Sciences. In: Kloeden, P., Pötzsche, C. (eds) Nonautonomous Dynamical Systems in the Life Sciences. Lecture Notes in Mathematics(), vol 2102. Springer, Cham. https://doi.org/10.1007/978-3-319-03080-7_1

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