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Tutorial of numerical continuation and bifurcation theory for systems and synthetic biology
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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 analysing the dynamics of nonlinear models by algorithmically detecting bifurcations. Here we aim to promote the use of numerical continuation tools by providing an introduction to nonlinear dynamics and numerical bifurcation analysis. Many numerical continuation packages are available, covering a wide range of system classes; a review of these packages is provided, to help both new and experienced practitioners in choosing the appropriate software tools for their needs.
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Cited by 1 Pith paper
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Continuation methods as a tool for parameter inference in electrophysiology modeling
Using continuation methods to follow a converged cardiac action potential limit cycle as parameters move in MCMC reduces a 40,000-iteration calibration from 12.4 hours to 3.7 hours on the tested toy model.
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