RESIDENCE TIME DISTRIBUTIONS FOR DOUBLE-SCROLL ATTRACTORS

Abstract

We investigated a choice of prototypical double-scroll attractors, namely trajectories resulting from Lorenz equations and from two sets of equations related to Chua's circuits. We found that the probability distribution for the residence times within a given scroll consists of prominent, exponentially decaying peaks. Similar peaks had been reported for stochastically resonant systems, which are driven periodically; however, in view of our results in autonomous systems, the appearance of such peaks has a higher degree of generality. In the systems we investigated, each peak corresponds to a subset of the attractor having a particular number of loops. Moreover, the sets of initial conditions leading to different peaks are interleaved in an analogous way as riddled or intermingled basins of attraction.