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Non-asymptotic-time Dynamics

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Physics of Biological Oscillators

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

Traditional analysis of dynamics concerns coordinate-invariant features of the long-time-asymptotic behaviour of a system. Using the non-autonomous Adler equation with slowly varying forcing, we illustrate three of the limitations of this traditional approach. We discuss an alternative, “slow-fast finite-time dynamical systems” approach, that is more suitable for slowly time-dependent one-dimensional phase dynamics, and is likely to be suitable for more general dynamics of open systems involving two or more timescales.

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Acknowledgements

We are grateful for the comments of three anonymous referees, which have led to considerable improvement of this manuscript. This study has been supported by an EPSRC Doctoral Prize Fellowship, the DFG grant CRC 701, the EPSRC grant EP/M006298/1, and the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 642563. Codes for the numerics carried out in this chapter are available upon request and are deposited on the Lancaster Publications and Research system Pure.

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Authors and Affiliations

  1. Exeter University, Exeter, UK

    Julian M. I. Newman

  2. Aix-Marseille University, Marseille, France

    Maxime Lucas

  3. Lancaster University, Lancaster, UK

    Aneta Stefanovska

Authors
  1. Julian M. I. Newman
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  2. Maxime Lucas
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  3. Aneta Stefanovska
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Correspondence to Julian M. I. Newman .

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Editors and Affiliations

  1. Department of Physics, Lancaster University, Lancaster, UK

    Aneta Stefanovska

  2. Department of Physics, Lancaster University, Lancaster, UK

    Peter V. E. McClintock

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Newman, J.M.I., Lucas, M., Stefanovska, A. (2021). Non-asymptotic-time Dynamics. In: Stefanovska, A., McClintock, P.V.E. (eds) Physics of Biological Oscillators. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-59805-1_7

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