Emergence of bimodality in noisy systems with single-well potential
M. Smoluchowski Institute of Physics, and Mark Kac Center for Complex Systems Research, Jagellonian University, ul. Reymonta 4, 30–, 059 Kraków, Poland
2 Institut für Physik, Humboldt-Universität zu Berlin, Newtonstrasse 15, 12489 Berlin, Germany
Revised: 27 April 2007
Published online: 6 June 2007
We study the stationary probability density of a Brownian particle in a potential with a single-well subject to the purely additive thermal and dichotomous noise sources. We find situations where bimodality of stationary densities emerges due to presence of dichotomous noise. The solutions are constructed using stochastic dynamics (Langevin equation) or by discretization of the corresponding Fokker-Planck equations. We find that in models with both noises being additive the potential has to grow faster than |x| in order to obtain bimodality. For potentials ∝|x| stationary solutions are always of the double exponential form.
PACS: 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.) / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.50.-r – Probability theory, stochastic processes, and statistics / 05.40.Ca – Noise
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007