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Nonlinearity and Biology

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Emerging Frontiers in Nonlinear Science

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 32))

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Abstract

In this chapter we discuss the origin and role of nonlinearities in some classes of biological models. We describe underlying biological mechanisms that generate nonlinearities and how they have been modeled in subfields, such as ecology and epidemiology. We present examples of recent models to highlight the importance of indirect effects and the emergence of alternative stable states, and trade offs. At the same time, we emphasize recent developments and unresolved challenges in biological modeling, such as data-theory coupling, parameter estimation and the generalization of results from low- to high-dimensional systems. We finish with recent examples of mathematical models of the glucose-insulin regulatory system, cancer treatment, limb development and pattern formation, and DNA.

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Acknowledgements

We gratefully acknowledge support through grants NSF-DMS-1815764 and UIUC RB17060.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL, 61801, USA

    Zoi Rapti

  2. Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, 1206 W. Gregory Drive, Urbana, IL, 61801, USA

    Zoi Rapti

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  1. Zoi Rapti
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Correspondence to Zoi Rapti .

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Editors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, USA

    Panayotis G. Kevrekidis

  2. Grupo de Fisica No Lineal, Departamento de Fisica Aplicada I, Escuela Politécnica Superior, Universidad de Sevilla, Seville, Spain

    Jesús Cuevas-Maraver

  3. Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA

    Avadh Saxena

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Rapti, Z. (2020). Nonlinearity and Biology. In: Kevrekidis, P., Cuevas-Maraver, J., Saxena, A. (eds) Emerging Frontiers in Nonlinear Science. Nonlinear Systems and Complexity, vol 32. Springer, Cham. https://doi.org/10.1007/978-3-030-44992-6_1

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