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Tutorial of numerical continuation and bifurcation theory for systems and synthetic biology

Blyth, Mark; Renson, Ludovic; Marucci, Lucia


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    <subfield code="u">Department of Mechanical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK</subfield>
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    <subfield code="u">Department of Engineering Mathematics, University of Bristol, Bristol BS8 1UB, UK - School of Cellular and Molecular Medicine, University of Bristol, Bristol BS8 1TD, UK - BrisSynBio, Bristol BS8 1TQ, UK</subfield>
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    <subfield code="a">&lt;p&gt;&lt;strong&gt;Abstract&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;Mathematical modelling allows us to concisely describe fundamental principles in biology. Analysis of models can help to both explain known phenomena, and predict the existence of new, unseen behaviours. Model analysis is often a complex task, such that we have little choice but to approach the problem with computational methods. Numerical continuation is a computational method for&amp;nbsp;analysing the dynamics of nonlinear models by algorithmically detecting bifurcations. Here we aim&amp;nbsp;to promote the use of numerical continuation tools by providing an introduction to nonlinear dynamics&amp;nbsp;and numerical bifurcation analysis. Many numerical continuation packages are available,&amp;nbsp;covering a wide range of system classes; a review of these packages is provided, to help both new and&amp;nbsp;experienced practitioners in choosing the appropriate software tools for their needs.&lt;/p&gt;</subfield>
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