A crisis of a stochastic web

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).