Chaotic Attractors of an Infinite-Dimensional Dynamical System

Abstract:

We study the chaotic attractors of a delay differential equation. The dimension of several attractors computed directly from the definition agrees to experimental resolution ~viththe dimension computed from the spectrum of Lyapunov exponents according to a conjecture of Kaplan and Yorke. Assuming this conjecture to be valid, as the delay parameter is varied, from computations of the spectrum of Lyapunov exponents, we observe a roughly linear increase from two to twenty in the dimension, while lhe metric entropy remains roughly constant. These results are compared to a linear analysis, and the asymptotic behavior of the Lyapunov exponents is derived.