Document Detail

An analysis of the reliability phenomenon in the FitzHugh-Nagumo model.
MedLine Citation:
PMID:  12435921     Owner:  NLM     Status:  MEDLINE    
The reliability of single neurons on realistic stimuli has been experimentally confirmed in a wide variety of animal preparations. We present a theoretical study of the reliability phenomenon in the FitzHugh-Nagumo model on white Gaussian stimulation. The analysis of the model's dynamics is performed in three regimes-the excitable, bistable, and oscillatory ones. We use tools from the random dynamical systems theory, such as the pullbacks and the estimation of the Lyapunov exponents and rotation number. The results show that for most stimulus intensities, trajectories converge to a single stochastic equilibrium point, and the leading Lyapunov exponent is negative. Consequently, in these regimes the discharge times are reliable in the sense that repeated presentation of the same aperiodic input segment evokes similar firing times after some transient time. Surprisingly, for a certain range of stimulus intensities, unreliable firing is observed due to the onset of stochastic chaos, as indicated by the estimated positive leading Lyapunov exponents. For this range of stimulus intensities, stochastic chaos occurs in the bistable regime and also expands in adjacent parts of the excitable and oscillating regimes. The obtained results are valuable in the explanation of experimental observations concerning the reliability of neurons stimulated with broad-band Gaussian inputs. They reveal two distinct neuronal response types. In the regime where the first Lyapunov has negative values, such inputs eventually lead neurons to reliable firing, and this suggests that any observed variance of firing times in reliability experiments is mainly due to internal noise. In the regime with positive Lyapunov exponents, the source of unreliable firing is stochastic chaos, a novel phenomenon in the reliability literature, whose origin and function need further investigation.
Efstratios K Kosmidis; K Pakdaman
Publication Detail:
Type:  Comparative Study; Journal Article; Research Support, Non-U.S. Gov't    
Journal Detail:
Title:  Journal of computational neuroscience     Volume:  14     ISSN:  0929-5313     ISO Abbreviation:  J Comput Neurosci     Publication Date:    2003 Jan-Feb
Date Detail:
Created Date:  2002-11-18     Completed Date:  2003-03-07     Revised Date:  2007-11-15    
Medline Journal Info:
Nlm Unique ID:  9439510     Medline TA:  J Comput Neurosci     Country:  United States    
Other Details:
Languages:  eng     Pagination:  5-22     Citation Subset:  IM    
Inserm U444, Université Paris 6, 27 rue Chaligny, 75571 Paris Cedex 12, France.
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MeSH Terms
Computer Simulation
Evaluation Studies as Topic
Models, Neurological*
Neural Networks (Computer)*
Neurons / physiology
Nonlinear Dynamics
Normal Distribution
Reproducibility of Results
Stochastic Processes*
Time Factors

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