Skip to main content

A survey of dynamical complexity in a mean-field nonlinear model of human EEG

A recently proposed mean-field mesoscopic theory of mammalian cortex dynamics describes the salient features of rhytmic electrical activity in the cerebral macrocolumn, with the use of inhibitory and excitatory neuronal populations [1]. This model is capable of producing a range of important human EEG (electroencephalogram) features such as the alpha rhythm, the 40 Hz activity thought to be associated with conscious awareness [2] and the changes in EEG spectral power associated with general anesthetic effect (e.g. the so-called "biphasic" response) [3]. From the point of view of nonlinear dynamics, the model entails a vast parameter space within which multistability, pseudoperiodic regimes, different routes to chaos, fat fractals and resonances occur for a range of physiologically relevant parameter values, giving rise to a multitude of rich and elaborate bifurcation scenarios. Examples of these are the Shilnikov saddle-node bifurcation (see Figure 1 and [4]), the homoclinic doubling cascade and different kinds of resonances. The origin and the character of these complex behaviors and their relevance for EEG activity are illustrated.

Figure 1

The largest Lyapunov exponent in color reproduced from [4], with superimposed two-parameter continuation of saddle-node and period-doubling bifurcations for periodic orbits of a mesoscopic mean field EEG model. The leftmost wedge of chaos terminates for negative values of the exterior forcings p ee and p ei .


  1. 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.

    Article  Google Scholar 

  2. 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.

    Article  Google Scholar 

  3. 3.

    Bojak I, Liley DTJ: Modeling the effects of anesthesia on the electroencephalogram. Phys Rev E. 2005, 71: 041902(1–22)

    Google Scholar 

  4. 4.

    van Veen L, Liley DTJ: Chaos via Shilnikov's saddle-node bifurcation in a theory of the electroencephalogram. Phys Rev Lett. 2006, 97: 208101(1–4)

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Federico Frascoli.

Rights and permissions

Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Frascoli, F., Van Veen, L., Bojak, I. et al. A survey of dynamical complexity in a mean-field nonlinear model of human EEG. BMC Neurosci 10, P285 (2009).

Download citation


  • Salient Feature
  • Complex Behavior
  • Spectral Power
  • Neuronal Population
  • Dynamical Complexity