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  • Open Access

Emergent phenomena in human EEG: a bifurcation theory approach

  • 1,
  • 2,
  • 3,
  • 1 and
  • 1
BMC Neuroscience200910 (Suppl 1) :P286

  • Published:


  • Bifurcation Diagram
  • Bifurcation Parameter
  • Neural Population
  • Emergent Phenomenon
  • Dynamical Requirement

A recently proposed mesoscopic mean-field theory of mammalian cortex electro-rhythmogenesis describes the salient features of electrical activity in the cerebral macrocolumn, with the use of inhibitory and excitatory neuronal populations [1]. Numerical solutions to the defining non-linear equations have revealed two interesting emergent phenomena: i) the appearance of large-scale spatial coherent 40 Hz oscillations in the model cortex, which has shown to be experimentally related to cognitive activity [2], and ii) a surge in spectral EEG power – when the brain is subject to general anesthetics – as a function of their concentration [3], a clinically established effect known as the "biphasic" response. Given that quasi-linear approximations have been unable to capture the dynamical mechanism that trigger these phenomena, a bifurcation analysis [4] of physiologically relevant parameter sets was performed.

Because of the predicted importance of inhibitory-inhibitory population strength in determining many fundamental dynamical features of the model, bifurcation parameters were chosen that modified inhibitory post-synaptic potential amplitudes and anatomical coupling strengths of the inhibitory neural population (respectively R and k in Figure 1). The analysis revealed the existence of a pattern of recurring bifurcation diagrams and specific "phase" transitions that constitute the dynamical requirements for the genesis and unfolding of 40 Hz and biphasic behaviors. This result also reaffirms the relevance of inhibition for the genesis of global collaborative events in the cortex and sheds light on the organization of the parameter space and the variability of EEG in the model respect to those perturbations and collective responses that are physiologically admissible.
Figure 1
Figure 1

An example of codimension two bifurcation plots for a parameter set displaying coherent gamma oscillations. The right-most branch of Hopf points corresponds to the emergence of approximately 37 Hz limit cycle activity via a subcritical Hopf bifurcation above the point labeled "gh" (generalized Hopf). Also, a homoclinic doubling cascade takes place along the line of homoclinics emanating from "bt" (Bogdanov-Takens point).

Authors’ Affiliations

Brain Sciences Institute (BSI), Swinburne University of Technology, P.O. Box 218, Victoria, 3122, Australia
Department of Mathematics and Statistics, Faculty of Arts and Sciences, Concordia University, 1455 de Maisonneuve Blvd. W., H3G 1M8 Montreal, Quebec, Canada
Donders Institute for Brain, Cognition and Behaviour, Centre for Neuroscience, Radboud University Nijmegen (Medical Centre), P.O. Box 9101//126, 6500, HB, Nijmegen, The Netherlands


  1. Liley DTJ, Cadusch PJ, Dafilis MP: A spatially continuous mean field theory of electrocortical activity. Network: Comput Neural Syst. 2002, 13: 67-113. 10.1088/0954-898X/13/1/303.View ArticleGoogle Scholar
  2. Bojak I, Liley DTJ: Self-organized 40 hz synchronization in a physiological theory of EEG. Neurocomp. 2007, 70: 2085-2090. 10.1016/j.neucom.2006.10.087.View ArticleGoogle Scholar
  3. Bojak I, Liley DTJ: Modeling the effects of anesthesia on the electroencephalogram. Phys Rev E. 2005, 71: 041902(1–22).Google Scholar
  4. Kuznetsov YA: Elements of applied bifurcation theory. 2004, New York, Springer-Verlag, 3View ArticleGoogle Scholar


© Frascoli et al; licensee BioMed Central Ltd. 2009

This article is published under license to BioMed Central Ltd.