PhysicaA348(2005)85–96 Analog study of the first passage time problem driven by power-law distributed noise M.P. da Silva Jr., M.L. Lyra à , M.V.D. Vermelho Departamento de Fı´sica, Universidade Federal de Alagoas, 57072-970 Maceio´, AL, Brazil Received 28 May 2004; received in revised form 28 July 2004 Available online 27 October 2004 Abstract In this work, we develop an analog circuit to generate a stochastic signal with stationary distribution exhibiting a tunable power-law tail. The proposed circuit design is a variant of a recentlyintroducedonebasedonadifferentialequationwithbothmultiplicativeandadditive noises. Here, the circuit is carefully designed in order to ensure that all components operate within their specific regimes. We provide a detailed characterization of the output signal, including the power-law exponent dependence on the tunable component. We apply the presentcircuittostudythefirstpassagetimeprobleminasimpleintegrate-firemodelofneural dynamics driven by a non-Gaussian noise. r 2004 Elsevier B.V. All rights reserved. PACS: 05.40.Ca; 05.40.Fb; 05.10.Gg; 84.30.Bv Keywords: Nonlinear dynamics; Multiplicative noise; Analog simulation 1. Introduction Non-linear dynamical systems can present a diversity of unconventional features whenperturbedbyanexternalnoise [1],suchasanenhancingoftransportproperties [2], stabilization of spatial patterns [3] and noise-induced phase transitions [4].In ARTICLE IN PRESS www.elsevier.com/locate/physa 0378-4371/$-see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2004.09.042 à Corresponding author. Fax: +55822141645. E-mail address: marcelo@fis.ufal.br (M.L. Lyra).