https://doi.org/10.1140/epjst/e2014-02310-0
Regular Article
Scaling properties and universality in a ratchet system
1 Departamento de Física, UNESP, Univ Estadual Paulista Av.24A, 1515, 13506-900 Rio Claro, SP, Brazil
2 UNESP, Univ Estadual Paulista, Câmpus de São João da Boa Vista, São João da Boa Vista, SP, Brazil
3 The Abdus Salam, ICTP, Strada Costiera, 11, 34151 Trieste, Italy
a e-mail: julianoantonio@sjbv.unesp.br
Received: 3 July 2014
Revised: 17 October 2014
Published online: 10 December 2014
Critical exponents that describe a transition from unlimited to limited diffusion for a ratchet system are obtained analytically and numerically. The system is described by a two dimensional nonlinear mapping with three relevant control parameters. Two of them control the non-linearity while the third one controls the intensity of the dissipation. Chaotic attractors appear in the phase space due to the dissipation and considering large non-linearity are characterised by the use of Lyapunov exponents. The critical exponents are used to overlap different curves of average momentum (dynamical variable) onto a single plot confirming a scale invariance. The formalism used is general and the procedure can be extended to different systems.
© EDP Sciences, Springer-Verlag, 2014
