Eur. Phys. J. D 29, 285-292 (2004)
https://doi.org/10.1140/epjd/e2004-00030-6

A crisis of a stochastic web

¹ Institute of Plasma Physics, Chinese Academy of Sciences, P.O. Box 1126, Hefei 230031, P.R. China
² College of Physics Science and Technology, Yangzhou University, Yangzhou 225002, P.R. China
³ CCAST(World Laboratory), P.O. Box 8730, Beijing 100080, P.R. China

Corresponding author: ^a drhe@mail.yzu.edu.cn

Received: 23 April 2003
Revised: 13 December 2003
Published online: 9 March 2004

Abstract

In a kicked rotor subjected to a piecewise-continuous force field, it is observed that a stochastic web and the chaotic diffusion on it suddenly change to transients when an adjustable parameter drives the dissipation. This phenomenon appears to be a new crisis type, which occurs in systems where conservative dynamics may be converted to a dissipative one with a contraction rate showing linear time dependence. It is analytically and numerically shown that, in the crisis, the lifetime dependence obeys universal scaling law suggested by Grebogy, Ott, and Yorke [Phys. Rev. Lett. 57, 1284 (1986)], and the scaling exponent takes a special value, 1, due to the dissipation characteristics. Additionally presented is another power law that describes, from another viewpoint, the transition of a conservative stochastic web (which is a fat fractal) to a non-attracting thin fractal (the strange repeller).