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Neuropercolation and Neural Population Models

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Encyclopedia of Computational Neuroscience

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Definition

Neuropercolation is a family of probabilistic models based on the mathematical theory of probabilistic cellular automata on lattices and random graphs. Neuropercolation is motivated by the structural and dynamical properties of large-scale neural populations. Neuropercolation extends the concept of phase transitions to interactive neural populations exhibiting frequent sudden transitions in their spatiotemporal dynamics. Neuropercolation develops equations for the probability distributions of macroscopic state variables by generalizing percolation theory as an alternative to models based on differential equations.

Mathematical Description of Neuropercolation

Neuropercolation uses the tools of random graphs and percolation theory developed over the past 50 years to establish a rigorous model of brain networks with complex dynamics (Erdos and Renyi 1960; Bollobás 1985; Bollobas and Riordan 2006). Neuropercolation is a natural domain for modeling collective properties of brain...

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, University of Memphis, Memphis, TN, USA

    Prof. Robert Kozma

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  1. Prof. Robert Kozma
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Correspondence to Robert Kozma .

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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Kozma, R. (2013). Neuropercolation and Neural Population Models. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_71-1

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  • DOI: https://doi.org/10.1007/978-1-4614-7320-6_71-1

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  • Publisher Name: Springer, New York, NY

  • Online ISBN: 978-1-4614-7320-6

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