© 2010

Modeling Phase Transitions in the Brain

  • D. Alistair Steyn-Ross
  • Moira Steyn-Ross

Part of the Springer Series in Computational Neuroscience book series (NEUROSCI, volume 4)

Table of contents

  1. Front Matter
    Pages i-xxix
  2. D.A. Steyn-Ross, M.L. Steyn-Ross, M.T. Wilson, J.W. Sleigh
    Pages 1-26
  3. D.T.J. Liley, I. Bojak, M.P. Dafilis, L. van Veen, F. Frascoli, B.L. Foster
    Pages 117-145
  4. Hans Liljenström
    Pages 147-177
  5. P.A. Robinson, C.J. Rennie, A.J.K. Phillips, J.W. Kim, J.A. Roberts
    Pages 179-201
  6. J.W. Sleigh, M.T. Wilson, L.J. Voss, D.A. Steyn-Ross, M.L. Steyn-Ross, X. Li
    Pages 203-221
  7. M.T. Wilson, M.L. Steyn-Ross, D.A. Steyn-Ross, J.W. Sleigh, I.P. Gillies, D.J. Hailstone
    Pages 223-242
  8. M.L. Steyn-Ross, D.A. Steyn-Ross, M.T. Wilson, J.W. Sleigh
    Pages 271-299
  9. Back Matter
    Pages 301-305

About this book


Foreword by Walter J. Freeman.

The induction of unconsciousness using anesthetic drugs demonstrates that the cerebral cortex can operate in two very different  modes: alert and responsive versus unaware and quiescent.  But the states of wakefulness and sleep are not single-neuron properties---they emerge as bulk properties of cooperating populations of neurons, with the switchover between states being similar to the physical change of phase observed when water freezes or ice melts.  Some brain-state transitions, such as sleep cycling, anesthetic induction, epileptic seizure, are obvious and detected readily with a few EEG electrodes; others, such as the emergence of gamma rhythms during cognition, or the ultra-slow BOLD rhythms of relaxed free-association, are much more subtle.  The unifying theme of this book is the notion that all of these bulk changes in brain behavior can be treated as phase transitions between distinct brain states.

"Modeling Phase Transitions in the Brain" contains chapter contributions from leading researchers who apply state-space methods, network models, and biophysically-motivated continuum approaches to investigate a range of neuroscientifically relevant problems that include analysis of nonstationary EEG time-series; network topologies that limit epileptic spreading; saddle--node bifurcations for anesthesia, sleep-cycling, and the wake--sleep switch; prediction of dynamical and noise-induced spatiotemporal instabilities underlying BOLD, alpha-, and gamma-band EEG oscillations, gap-junction-moderated Turing structures, and Hopf--Turing interactions leading to cortical waves. 

Written for:

Researchers, clinicians, physicians, neurologists

About the editors:

Alistair Steyn-Ross and Moira Steyn-Ross are computational and theoretical physicists in the Department of Engineering, University of Waikato, New Zealand.  They share a long-standing interest in the application of physics-based methods to gain insight into the emergent behavior of complex biological systems such as single neurons and interacting neural populations.


Cortex EEG Turing and Hopf behavior electro-cortical activity mean-field equations modular networks neurons

Editors and affiliations

  • D. Alistair Steyn-Ross
    • 1
  • Moira Steyn-Ross
    • 2
  1. 1.Dept. EngineeringUniversity of WaikatoHamiltonNew Zealand
  2. 2.Dept. EngineeringUniversity of WaikatoHamiltonNew Zealand

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From the book reviews:

“Excellent description of neurophysiology of dynamics systems, both linear and nonlinear. Highly recommended.” (Joseph J. Grenier,, October, 2014)