Abstract. Many dynamical systems are thought to exhibit windows of attracting periodic behaviour for arbitrarily small perturbations from parameter values yielding chaotic attractors. This structural instability of chaos is particularly well documented and understood for the case of the one-dimensional quadratic map. In this paper we attempt to numerically characterize the global parameter-space structure of the dense set of periodic `windows' occurring in the chaotic regime of the quadratic map. In particular, we use scaling techniques to extract information on the probability distribution of window parameter widths as a function of period and location of the window in parameter space. We also use this information to obtain the uncertainty exponent which is a quantity that globally characterizes the ability to identify chaos in the presence of small parameter uncertainties.

Print publication: Issue 20 (21 October 1997)
Received 4 September 1996, in final form 23 June 1997