caa a22 4500 445330112 CHVBK 20180317142734.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s00285-010-0391-3 doi (NATIONALLICENCE)springer-10.1007/s00285-010-0391-3 A decision-making Fokker-Planck model in computational neuroscience [Elektronische Daten] [José Carrillo, Stéphane Cordier, Simona Mancini] In computational neuroscience, decision-making may be explained analyzing models based on the evolution of the average firing rates of two interacting neuron populations, e.g., in bistable visual perception problems. These models typically lead to a multi-stable scenario for the concerned dynamical systems. Nevertheless, noise is an important feature of the model taking into account both the finite-size effects and the decision's robustness. These stochastic dynamical systems can be analyzed by studying carefully their associated Fokker-Planck partial differential equation. In particular, in the Fokker-Planck setting, we analytically discuss the asymptotic behavior for large times towards a unique probability distribution, and we propose a numerical scheme capturing this convergence. These simulations are used to validate deterministic moment methods recently applied to the stochastic differential system. Further, proving the existence, positivity and uniqueness of the probability density solution for the stationary equation, as well as for the time evolving problem, we show that this stabilization does happen. Finally, we discuss the convergence of the solution for large times to the stationary state. Our approach leads to a more detailed analytical and numerical study of decision-making models applied in computational neuroscience. Springer-Verlag, 2010 Computational neuroscience nationallicence Fokker-Planck equation nationallicence General relative entropy nationallicence Carrillo José ICREA (Institució Catalana de Recerca i Estudis Avançats), Bellaterra, Spain aut Cordier Stéphane Fédération Denis Poisson (FR 2964), Department of Mathematics (MAPMO UMR 6628), University of Orléans, BP. 6759, 45067, Orléans, France aut Mancini Simona Fédération Denis Poisson (FR 2964), Department of Mathematics (MAPMO UMR 6628), University of Orléans, BP. 6759, 45067, Orléans, France aut Journal of Mathematical Biology Springer-Verlag 63/5(2011-11-01), 801-830 0303-6812 63:5<801 2011 63 285 https://doi.org/10.1007/s00285-010-0391-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00285-010-0391-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Carrillo José ICREA (Institució Catalana de Recerca i Estudis Avançats), Bellaterra, Spain aut NATIONALLICENCE 700 1- Cordier Stéphane Fédération Denis Poisson (FR 2964), Department of Mathematics (MAPMO UMR 6628), University of Orléans, BP. 6759, 45067, Orléans, France aut NATIONALLICENCE 700 1- Mancini Simona Fédération Denis Poisson (FR 2964), Department of Mathematics (MAPMO UMR 6628), University of Orléans, BP. 6759, 45067, Orléans, France aut NATIONALLICENCE 773 0- Journal of Mathematical Biology Springer-Verlag 63/5(2011-11-01), 801-830 0303-6812 63:5<801 2011 63 285 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer