Time series analysis of homoclinic nonlinear systems using a wavelet transform method

Austin, James C; Healey, Jonathan J

Abstract

Homoclinic (and heteroclinic) trajectories are closed paths in phase space that connect one or more saddle points. They play an important role in the study of dynamical systems and are associated with the creation/destruction of limit cycles as a parameter is varied. Often, this creation/destruction process involves complicated sequences of bifurcations in small regions of parameter space and there is now an established theoretical framework for the study of such systems.

The eigenvalues of saddle points in the phase space determine the behaviour of the system. In this article we present a new eigenvalue estimation technique based on a wavelet transformation of a time series under study and compare it with an existing method based on phase space reconstruction. We find that the two methods give good agreement with theory using clean model data, but where noisy data are analysed the wavelet technique is both more robust and easier to implement.

Citation

Austin, J. C., & Healey, J. J. (2004). Time series analysis of homoclinic nonlinear systems using a wavelet transform method. Fluid Dynamics Research, 34(6), Article 401. https://doi.org/10.1016/j.fluiddyn.2004.03.002

• Journal Article Type: Article
• Publication Date: 2004
• Deposit Date: Jun 5, 2024
• Journal: Fluid Dynamics Research
• Print ISSN: 0169-5983
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 34
• Issue: 6
• Article Number: 401
• DOI: https://doi.org/10.1016/j.fluiddyn.2004.03.002
• Public URL: https://keele-repository.worktribe.com/output/845019
• Publisher URL: https://iopscience.iop.org/article/10.1016/j.fluiddyn.2004.03.002