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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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  <identifier identifierType="DOI">10.5281/zenodo.4835824</identifier>
  <creators>
    <creator>
      <creatorName>Blyth, Mark</creatorName>
      <givenName>Mark</givenName>
      <familyName>Blyth</familyName>
      <affiliation>Department of Engineering Mathematics, University of Bristol, Bristol BS8 1UB, UK.</affiliation>
    </creator>
    <creator>
      <creatorName>Renson, Ludovic</creatorName>
      <givenName>Ludovic</givenName>
      <familyName>Renson</familyName>
      <affiliation>Department of Mechanical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK</affiliation>
    </creator>
    <creator>
      <creatorName>Marucci, Lucia</creatorName>
      <givenName>Lucia</givenName>
      <familyName>Marucci</familyName>
      <affiliation>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</affiliation>
    </creator>
  </creators>
  <titles>
    <title>Tutorial of numerical continuation and bifurcation theory for systems and synthetic biology</title>
  </titles>
  <publisher>Zenodo</publisher>
  <publicationYear>2020</publicationYear>
  <dates>
    <date dateType="Issued">2020-08-12</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Preprint</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/4835824</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsVersionOf">10.5281/zenodo.4835823</relatedIdentifier>
    <relatedIdentifier relatedIdentifierType="URL" relationType="IsPartOf">https://zenodo.org/communities/cosy-bio</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="https://creativecommons.org/licenses/by/4.0/legalcode">Creative Commons Attribution 4.0 International</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">&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;</description>
  </descriptions>
  <fundingReferences>
    <fundingReference>
      <funderName>European Commission</funderName>
      <funderIdentifier funderIdentifierType="Crossref Funder ID">10.13039/501100000780</funderIdentifier>
      <awardNumber awardURI="info:eu-repo/grantAgreement/EC/H2020/766840/">766840</awardNumber>
      <awardTitle>Control Engineering of Biological Systems for Reliable Synthetic Biology Applications</awardTitle>
    </fundingReference>
  </fundingReferences>
</resource>
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