Mean first-passage time in a bistable system driven by multiplicative and additive colored noises with colored cross-correlation Xiaoyan Zhang * , Wei Xu * , Bingchang Zhou Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, China article info Article history: Received 7 September 2007 Received in revised form 29 January 2008 Accepted 27 February 2009 Available online 16 March 2009 PACS: 05.40.a Keywords: Mean first-passage time Bistable system Colored noise Color-correlated noise abstract The effect of any system parameter (include p, q, k, s 1 , s 2 , s 3 ) on the mean first-passage time is investigated in a symmetric bistable system driven by multiplicative and additive col- ored noise with colored cross-correlation. Expression of the mean first-passage time (MFPT) has been obtained by applying the steepest-descent approximation. The effects of the additive noise intensity and the multiplicative noise intensity on the MFPT are mostly different only with bigger positive values of the strength of correlations between multiplicative and additive noise; and the MFPT has a maximum with the increase of the multiplicative noise intensity. The effects of the noise self-correlation times on the MFPT are quite different from that of the correlation time between the noises as the strength of correlations between multiplicative and additive noise is positive. Crown Copyright Ó 2009 Published by Elsevier B.V. All rights reserved. 1. Introduction The white noise is a state of being ideal, so the system with colored noise is expected to be more physically realistic. More and more researchers are interested in the effect of colored noise on the stochastic systems, and the studies indicate that the systems will present more peculiar characteristics if it is driven by colored noise or colored cross-correlation noises [1–9]. Jung and Hanggi [3] investigated the bistable system driven by the colored noise and obtained the unified colored- noise approximation (UCNA). Jia and Li [5] considered the reentrance phenomena in a bistable model driven by colored cross-correlation noises. They found that the phenomenon can occur as the strength of correlation between two white noises varies. Luo and Zhu [6] studied correlated colored noises in one-dimensional nonlinear system. They found that the fluctuation in the system corresponding to positive and negative noise coupling strength exhibits a very different dependence on the noise correlation time. Jin and Xu [7] showed that the effects of the correlation time of multiplicative noise and the correlation time between the multiplicative and additive noises on the mean first-passage time of the system are different. The steady-state properties of the nonlinear kinetic model with colored cross-correlation between colored noises are investigated in Refs. [8,9]. They obtained the approximate Fokker–Planck equation and proved the validity of this result. Owing to the characteristic of colored noise, the dynamic process with colored noise is non-Markovian process. The pre- cise expression of Fokker–Planck equation cannot be obtained, and the researchers only got approximated result. So in this paper, we investigate the mean first-passage time (MFPT) of bistable kinetic system with colored noises on the basis of Refs. [8,9], and discuss the effects of noises on the MFPT. 1007-5704/$ - see front matter Crown Copyright Ó 2009 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.cnsns.2009.02.029 * Corresponding authors. Tel./fax: +86 298 849 5453. E-mail addresses: zhangxiaoyan320@mail.nwpu.edu.cn (X. Zhang), weixu@nwpu.edu.cn (W. Xu). Commun Nonlinear Sci Numer Simulat 14 (2009) 4220–4225 Contents lists available at ScienceDirect Commun Nonlinear Sci Numer Simulat journal homepage: www.elsevier.com/locate/cnsns