###
Joeri Jacobs, Edward Ott, and Brian R. Hunt

*
Phys. Rev. E 56 (1997), 6508-6515
*

Online abstract and download information

As a bifurcation parameter $\mu$ is varied it is common for chaotic
systems to display windows of width $\Delta\mu$ in which there is
stable periodic behavior. In this paper we examine the dependence of
the transient time tau of a periodic window (i.e., the typical time an
initial condition wanders around chaotically before settling into
periodic behavior) on the size of the periodic window $\Delta\mu$. We
argue and numerically verify that for one-dimensional maps with a
quadratic extremum $1/\tau ~ (\Delta\mu)^{1/2}$ and we find an
asymptotic universal form for the parameter dependence of tau within
individual high-period windows. For two-dimensional maps, we
conjecture that for small windows the scaling changes to $1/\tau ~
(\Delta\mu)^{d-1/2}$, where $d$ is a fractal dimension associated with
a typical attractor for chaotic parameter values near the considered
periodic windows.

Back to my list of recent papers.

Back to my home page.

*Last updated: June 23, 1998*