Abstract
Nonsmooth processes such as stick-slip may introduce problems with phase-space reconstructions. We examine chaotic single-degree-of-freedom stick-slip friction models and use the method of delays to reconstruct the phase space. We illustrate that this reconstruction process can cause pseudo trajectories to collapse in a way that is unlike, yet related to, the dimensional collapse in the original phase-space. As a result, the reconstructed attractor is not topologically similar to the real attractor. Standard dimensioning tools are applied in effort to recognize this situation. The use of additional observables is examined as a possible remedy for the problem.
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Feeny, B.F., Liang, J.W. Phase-Space Reconstructions and Stick-Slip. Nonlinear Dynamics 13, 39–57 (1997). https://doi.org/10.1023/A:1008245332549
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DOI: https://doi.org/10.1023/A:1008245332549