Journal
BIOLOGICAL CYBERNETICS
Volume 102, Issue 2, Pages 145-154Publisher
SPRINGER
DOI: 10.1007/s00422-009-0357-y
Keywords
False bifurcation; Canard; Delay differential equation; Continuation method; Dynamical system; Mixed-mode oscillations; Neural-field model; Absence epilepsy
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Funding
- EPSRC [EP/D068436/01, EP/E032249/01]
- EPSRC [EP/D068436/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/D068436/1] Funding Source: researchfish
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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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