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Chaos / Volume 21 / Issue 4 / FOCUS ISSUE: NONLINEAR AND STOCHASTIC PHYSICS IN BIOLOGY

Chaos 21, 047512 (2011); http://dx.doi.org/10.1063/1.3664409 (9 pages)

Vulnerability to paroxysmal oscillations in delayed neural networks: A basis for nocturnal frontal lobe epilepsy?

Austin Quan1, Ivan Osorio2, Toru Ohira3, and John Milton3

1Department of Mathematics, Harvey Mudd College, Claremont, California 91711, USA
2Department of Neurology, University of Kansas Medical Center, Kansas City, Kansas 66049, USA
3W. M. Keck Science Department, The Claremont Colleges, Claremont, California 91711, USA

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(Received 19 August 2011; accepted 8 November 2011; published online 29 December 2011)

Resonance can occur in bistable dynamical systems due to the interplay between noise and delay (τ) in the absence of a periodic input. We investigate resonance in a two-neuron model with mutual time-delayed inhibitory feedback. For appropriate choices of the parameters and inputs three fixed-point attractors co-exist: two are stable and one is unstable. In the absence of noise, delay-induced transient oscillations (referred to herein as DITOs) arise whenever the initial function is tuned sufficiently close to the unstable fixed-point. In the presence of noisy perturbations, DITOs arise spontaneously. Since the correlation time for the stationary dynamics is ∼τ, we approximated a higher order Markov process by a three-state Markov chain model by rescaling time as t → 2sτ, identifying the states based on whether the sub-intervals were completely confined to one basin of attraction (the two stable attractors) or straddled the separatrix, and then determining the transition probability matrix empirically. The resultant Markov chain model captured the switching behaviors including the statistical properties of the DITOs. Our observations indicate that time-delayed and noisy bistable dynamical systems are prone to generate DITOs as switches between the two attractors occur. Bistable systems arise transiently in situations when one attractor is gradually replaced by another. This may explain, for example, why seizures in certain epileptic syndromes tend to occur as sleep stages change.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. BACKGROUND
  3. RESULTS
  4. DISCUSSION

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KEYWORDS and PACS

Keywords

Markov processes, medical disorders, neural nets, neurophysiology, noise, probability, sleep, statistical analysis

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3664409

PUBLICATION DATA

ISSN

1054-1500 (print)  
1089-7682 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    C. W. Eurich and J. G. Milton, Phys. Rev. E 54, 6681 (1996).

    J. Foss, F. Moss, and J. Milton, Phys. Rev. E 55, 4536 (1997).

    C. Grotta-Ragazzo, K. Pakdaman, and C. P. Malta, Phys. Rev. E 60, 6230 (1999).

    K. Pakdaman, C. Grotta-Ragazzo, and C. P. Malta, Phys. Rev. E 58, 3623 (1998).

    T. Ohira and Y. Sato, Phys. Rev. Lett. 82, 8111 (1999).

    L. Tsimring and A. Pikovsky, Phys. Rev. Lett. 87, 250602 (2001).

    L. Gammaitoni, F. Marchesoni, E. Menichella-Saetta, and S. Santucci, Phys. Rev. Lett. 62, 349 (1989).

    L. Gammaitoni, P. Hänngi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. 70, 1223 (1998).

    M. I. Rabinovich, P. Varona, A. I. Selveston, and H. D. I. Abarbanel, Rev. Mod. Phys. 78, 1213 (2006).

    D. Pierson and F. Moss, Phys. Rev. Lett. 75, 2124 (1995).

    C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 57, 1284 (1986).

    S. M. Baer and E. M. Gaekel, Phys. Rev. E 78, 036205 (2008).


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