Scaling properties and universality in a ratchet system
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2014-12-01
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Oliveira, J. A. de [UNESP]
Leonel, E. D. [UNESP]
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Springer
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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.
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European Physical Journal-special Topics. Heidelberg: Springer Heidelberg, v. 223, n. 13, p. 2969-2978, 2014.