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Experimentally Viable Techniques for Accessing Coexisting Attractors Correlated with Lyapunov Exponents

Authors :
Joshua Ray Hall
Erikk Kenneth Tilus Burton
Dylan Michael Chapman
Donna Kay Bandy
Source :
Applied Sciences, Vol 11, Iss 21, p 9905 (2021)
Publication Year :
2021
Publisher :
MDPI AG, 2021.

Abstract

Universal, predictive attractor patterns configured by Lyapunov exponents (LEs) as a function of the control parameter are shown to characterize periodic windows in chaos just as in attractors, using a coherent model of the laser with injected signal. One such predictive pattern, the symmetric-like bubble, foretells of an imminent bifurcation. With a slight decrease in the gain parameter, we find the symmetric-like bubble changes to a curved trajectory of two equal LEs in one attractor, while an increase in the gain reverses this process in another attractor. We generalize the power-shift method for accessing coexisting attractors or periodic windows by augmenting the technique with an interim parameter shift that optimizes attractor retrieval. We choose the gain as our parameter to interim shift. When interim gain-shift results are compared with LE patterns for a specific gain, we find critical points on the LE spectra where the attractor is unlikely to survive the gain shift. Noise and lag effects obscure the power shift minimally for large domain attractors. Small domain attractors are less accessible. The power-shift method in conjunction with the interim parameter shift is attractive because it can be experimentally applied without significant or long-lasting modifications to the experimental system.

Details

Language :
English
ISSN :
20763417
Volume :
11
Issue :
21
Database :
Directory of Open Access Journals
Journal :
Applied Sciences
Publication Type :
Academic Journal
Accession number :
edsdoj.79cb29b17b9e4b9294781d94374b9c11
Document Type :
article
Full Text :
https://doi.org/10.3390/app11219905