LOCAL MINIMA-BASED RECURRENCE PLOTS FOR CONTINUOUS DYNAMICAL SYSTEMS
Abstract
A major issue in using recurrence plots (RPs) to study dynamical systems is the choice of neighborhood size for thresholding the distance matrix that creates the plot. This is particularly important for continuous dynamical systems as temporal correlations of the trajectory might provide redundant information for recurrence analysis. We suggest an alternative procedure for creating RPs using the local minima provided by the distance profile, which approximately corresponds to the recurrence information in the orthogonal direction. The local minima-based thresholding yields a clean RP of minimized line thickness, that is compared to the plot obtained by the standard radius bases thresholding. New definitions of line segments arising from the local minima-based method are outlined, which yield consistent results with those derived from standard methods. Our preliminary comparison suggests that the newly introduced thresholding technique is more sensitive to small changes in a system's dynamics. We demonstrate our method via the chaotic Lorenz system without the loss of generality.
References
- Rev. Mod. Phys. 65, 1331 (1993), DOI: 10.1103/RevModPhys.65.1331. Crossref, ISI, Google Scholar
- Phys. Lett. A 263, 299 (1999), DOI: 10.1016/S0375-9601(99)00751-3. Crossref, ISI, Google Scholar
- New J. Phys. 12, 033025 (2010), DOI: 10.1088/1367-2630/12/3/033025. Crossref, Google Scholar
- Europhys. Lett. 4, 973 (1987), DOI: 10.1209/0295-5075/4/9/004. Crossref, Google Scholar
- Chaos 9, 413 (1999), DOI: 10.1063/1.166424. Crossref, ISI, Google Scholar
- IEEE Trans. Instit. Electr. Engin. Japan C 122, 141 (2002). Google Scholar
- Phys. Rev. E 80, 026214 (2009), DOI: 10.1103/PhysRevE.80.026214. Crossref, Google Scholar
- J. Atmosph. Sci. 20, 120 (1963). ISI, Google Scholar
- Phys. Lett. A 302, 299 (2002), DOI: 10.1016/S0375-9601(02)01170-2. Crossref, ISI, Google Scholar
- Phys. Rev. E 66, 026702 (2002), DOI: 10.1103/PhysRevE.66.026702. Crossref, Google Scholar
- Phys. Rep. 438, 237 (2007), DOI: 10.1016/j.physrep.2006.11.001. Crossref, ISI, Google Scholar
- Phys. Lett. A 373, 4246 (2009), DOI: 10.1016/j.physleta.2009.09.042. Crossref, ISI, Google Scholar
- Int. J. Bifurcation and Chaos 21, 1003 (2011). Link, ISI, Google Scholar
- Acta Mathematica 13, 1 (1890). ISI, Google Scholar
- Phys. Lett. A 330, 214 (2004), DOI: 10.1016/j.physleta.2004.07.066. Crossref, ISI, Google Scholar
- The European Phys. J. — Special Topics 164, 45 (2008), DOI: 10.1140/epjst/e2008-00833-5. Crossref, ISI, Google Scholar
F. Takens , Detecting Strange Attractors in Turbulence,Lecture Notes in Mathematics (1981) pp. 366–381. Crossref, Google Scholar- , Tutorials in Contemporary Nonlinear Methods for the Behavioral Sciences Web Book, eds.
M. A. Riley and G. C. Van Orden (National Science Foundation, U.S., 2005) pp. 26–94, http://www.nsf.gov/sbe/bcs/pac/nmbs/nmbs.jsp. Google Scholar - Phys. Lett. A 171, 199 (1992), DOI: 10.1016/0375-9601(92)90426-M. Crossref, ISI, Google Scholar
- Int. J. Bifurcation and Chaos 17, 4273 (2007). Link, ISI, Google Scholar
| Remember to check out the Most Cited Articles! |
|---|
|
Check out our Bifurcation & Chaos |
