Definition
The Fokker-Planck equation (FPE) is a partial differential equation that describes the temporal evolution of the probability distribution of a stochastic variable. It is useful to describe the membrane potential distribution of a neuron receiving stochastic inputs. In this context, it has been used to determine stationary firing rates as well as neuronal responses to time-dependent stimulations. Beyond its application to single neuron dynamics, the FPE is useful to analyze in a self-consistent way the behavior of an ensemble of interacting spiking neurons and in particular the emergence of neural rhythms.
Historical Remarks
The Fokker-Planck equation is named after Adriaan Fokker and Max Planck who introduced it to describe the time evolution of the velocity probability distribution for a Brownian particle. Marian Smoluchowski used it to analyze the position...
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References
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Brunel, N., Hakim, V. (2014). Fokker-Planck Equation. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_60-2
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DOI: https://doi.org/10.1007/978-1-4614-7320-6_60-2
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Fokker-Planck Equation- Published:
- 01 August 2014
DOI: https://doi.org/10.1007/978-1-4614-7320-6_60-2
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Fokker-Planck Equation- Published:
- 07 February 2014
DOI: https://doi.org/10.1007/978-1-4614-7320-6_60-1