Abstract
Nonlinear delay-differential equations (DDE’s), such as the Mackey-Glass or the Ikeda equations, are strongly multistable when the delay-to-response time ratio is large and have an attractor dimension that increases with the delay. We discuss how properties such as dynamical invariants and multistability can be studied using linear stability analysis and power spectra. As the delay increases, the spectrum converges to an exponentially decaying envelope with a superimposed periodic modulation. Linear stability analysis can predict the position of the peaks of this modulation and quantify multistability. Also, the number of peaks in the power spectrum and the number of linear modes within an inverse characteristic autocorrelation time can be used to estimate the attractor dimension.
Published Version
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