Intermittency and deterministic diffusion in chaotic ratchets Jos  e L. Mateos * Instituto de F  ısica, Universidad Nacional Aut onoma de M exico, Apartado Postal 20-364, 01000 M exico, D.F., Mexico Abstract We consider the problem of deterministic transport of particles in an asymmetric periodic ratchet po- tential of the rocking type. When the inertial term is taken into account, the dynamics can be chaotic and modify the transport properties. We calculate the bifurcation diagram as a function of the amplitude of forcing and analyze in detail the crisis bifurcation that leads to current reversals. Near this bifurcation we obtain intermittency and anomalous deterministic diffusion. Ó 2003 Elsevier B.V. All rights reserved. PACS: 05.45.Ac; 05.40.Fb; 05.45.Pq; 05.60.Cd Keywords: Ratchets; Chaotic transport; Intermittency; Deterministic diffusion; Brownian motors 1. Introduction Recent advances in nonequilibrium statistical physics have revealed various instances of the surprising phenomenon of noise enhanced order, such as stochastic resonance [1,2], Brownian motors or noise-induced transport [3–5]. These remarkable phenomena occur due to the con- structive role of noise in nonlinear dynamical systems [6]. Noise-induced, directed transport in a spatially periodic system in thermal equilibrium is ruled out by the second law of thermodynamics. Therefore, in order to generate transport, the system has to be driven away from thermal equilibrium by an additional deterministic or stochastic force. In the most interesting situation, these forces are unbiased, that is, their temporal, spatial or ensemble averages vanish. Besides the breaking of thermal equilibrium, another important re- quirement to get directed transport in a spatially periodic system is the breaking of the spatial inversion symmetry. We speak then of Brownian motors, ratchet devices, or, in the biological * Tel.: +52-55-5622-5130; fax: +52-55-5622-5015. E-mail address: mateos@fisica.unam.mx (J.L. Mateos). 1007-5704/03/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/S1007-5704(03)00042-X Communications in Nonlinear Science and Numerical Simulation 8 (2003) 253–263 www.elsevier.com/locate/cnsns