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A method for detecting false bifurcations in dynamical systems: application to neural-field models

Research output: Contribution to journalArticlepeer-review

Serafim Rodrigues, David Barton, Frank Marten, Moses Kibuuka, Gonzalo Alarcon, Mark P. Richardson, John R. Terry

Original languageEnglish
Pages (from-to)145 - 154
Number of pages10
JournalBiological Cybernetics
Volume102
Issue number2
DOIs
PublishedFeb 2010

King's Authors

Abstract

In this article, we present a method for tracking changes in curvature of limit cycle solutions that arise due to inflection points. In keeping with previous literature, we term these changes false bifurcations, as they appear to be bifurcations when considering a Poincar, section that is tangent to the solution, but in actual fact the deformation of the solution occurs smoothly as a parameter is varied. These types of solutions arise commonly in electroencephalogram models of absence seizures and correspond to the formation of spikes in these models. Tracking these transitions in parameter space allows regions to be defined corresponding to different types of spike and wave dynamics, that may be of use in clinical neuroscience as a means to classify different subtypes of the more general syndrome.

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