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Chaos, Neural Population Models and

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Encyclopedia of Computational Neuroscience

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Definition

Nonlinear dynamic systems, even if completely described by deterministic equations, may exhibit unpredictable behavior, in that arbitrarily small deviations in the initial conditions, after sufficient time has passed, lead to completely different behavior. This is referred to as deterministic chaos and has been shown to arise in neural population models (NPM).

Detailed Description

Chaotic Systems

Deterministic chaos occurs in systems completely described by deterministic differential equations. These systems may be quite simple, but they have to be nonlinear and live in phase spaces of at least three dimensions (Poincaré-Bendixson theorem). Chaos means that arbitrarily small differences in initial conditions nevertheless lead to strongly diverging trajectories of system behavior after some time. Consequently, under any realistic conditions the system’s long-term behavior is unpredictable. In spite of the impossibility to predict the system’s behavior in any single case, the...

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Authors and Affiliations

  1. Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany

    Dr. Thomas R. Knösche

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  1. Dr. Thomas R. Knösche
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Correspondence to Thomas R. Knösche .

Editor information

Editors and Affiliations

  1. Atlanta, Georgia, USA

    Dieter Jaeger

  2. Department of Biomedical Engineering, Florida International University, Miami, Florida, USA

    Ranu Jung

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Knösche, T.R. (2014). Chaos, Neural Population Models and. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_54-2

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  • DOI: https://doi.org/10.1007/978-1-4614-7320-6_54-2

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  • Publisher Name: Springer, New York, NY

  • Online ISBN: 978-1-4614-7320-6

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Chapter history

  1. Latest

    Chaos, Neural Population Models and
    Published:
    28 July 2014

    DOI: https://doi.org/10.1007/978-1-4614-7320-6_54-2

  2. Original

    Chaos, Neural Population Models and
    Published:
    07 February 2014

    DOI: https://doi.org/10.1007/978-1-4614-7320-6_54-1

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