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Chaos via Shilnikov's saddle-node bifurcation in a theory of the electroencephalogram
Lennaert van Veen1, David T J Liley
1Department of Mathematical and Statistical Science, La Trobe University, Victoria 3086, Australia. l.vanveen@latrobe.edu.au
Abstract:
We study the bifurcation diagram of a mesoscopic model of the human cortex. This model is known to exhibit robust chaotic behavior in the space of parameters that model exterior forcing. We show that the bifurcation diagram has an unusual degree of organization. In particular, we show that the chaos is spawned by a codimension-one homoclinic bifurcation that was analyzed by Shilnikov in 1969 but has never before been found in a physical application.
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