title: Approximating chaotic saddles for delay differential equations.
abstract: Chaotic saddles are unstable invariant sets in the phase space of dynamical systems that exhibit transient chaos. They play a key role in mediating transport processes involving scattering and chaotic transients. Here we present evidence (long chaotic transients and fractal basins of attraction) of transient chaos in a "logistic" delay differential equation. We adapt an existing method (stagger-and-step) to numerically construct the chaotic saddle for this system. This is the first such analysis of transient chaos in an infinite-dimensional dynamical system, and in delay differential equations in particular. Using Poincaré section techniques we illustrate approaches to visualizing the saddle set, and confirm that the saddle has the Cantor-like fractal structure consistent with a chaotic saddle generated by horseshoe-type dynamics.
authors.affiliation: Thompson Rivers University, Kamloops, British Columbia V2C 5N3, Canada.
authors.forename: S Richard
authors.initials: SR
authors.lastname: Taylor
authors.forename: Sue Ann
authors.initials: SA
authors.lastname: Campbell