A decision-making Fokker-Planck model in computational neuroscience
Carrillo de la Plata, José Antonio (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Cordier, Stéphane (University of Orleans. Department of Mathematics)
Mancini, Simona (University of Orleans. Department of Mathematics)
Centre de Recerca Matemàtica

Publicación:	Centre de Recerca Matemàtica 2010
Descripción:	25 p.
Resumen:	Minimal models for the explanation of decision-making in computational neuroscience are based on the analysis of the evolution for the average firing rates of two interacting neuron populations. While these models typically lead to multi-stable scenario for the basic derived dynamical systems, noise is an important feature of the model taking into account finite-size effects and robustness of the decisions. These stochastic dynamical systems can be analyzed by studying carefully their associated Fokker-Planck partial differential equation. In particular, we discuss the existence, positivity and uniqueness for the solution of the stationary equation, as well as for the time evolving problem. Moreover, we prove convergence of the solution to the the stationary state representing the probability distribution of finding the neuron families in each of the decision states characterized by their average firing rates. Finally, we propose a numerical scheme allowing for simulations performed on the Fokker-Planck equation which are in agreement with those obtained recently by a moment method applied to the stochastic differential system. Our approach leads to a more detailed analytical and numerical study of this decision-making model in computational neuroscience.
Derechos:	Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús
Lengua:	Anglès
Colección:	Centre de Recerca Matemàtica. Prepublicacions
Colección:	Prepublicacions del Centre de Recerca Matemàtica ; 919
Documento:	Article ; Prepublicació ; Versió de l'autor
Materia:	Neurociència computacional ; Entropia

25 p, 415.3 KB

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