Abstract
Original language | English |
---|---|
Pages (from-to) | 4273-4283 |
Number of pages | 11 |
Journal | International Journal of Bifurcation and Chaos |
Volume | 17 |
Issue number | 12 |
DOIs | |
Publication status | Published - Dec 2007 |
Fingerprint
Keywords
- recurrence plot
- analytic description
- quasiperiodic motion
- nontrivial recurrence
Cite this
Analytical description of recurrence plots of dynamical systems with nontrivial recurrences. / Zou, Y.; Thiel, Marco; Romano , M Carmen; Kurths, Jurgen.
In: International Journal of Bifurcation and Chaos, Vol. 17, No. 12, 12.2007, p. 4273-4283.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Analytical description of recurrence plots of dynamical systems with nontrivial recurrences
AU - Zou, Y.
AU - Thiel, Marco
AU - Romano , M Carmen
AU - Kurths, Jurgen
PY - 2007/12
Y1 - 2007/12
N2 - In this paper we study recurrence plots (RPs) for the simplest example of nontrivial recurrences, namely in the case of a quasiperiodic motion. This case can be still studied analytically and constitutes a link between simple periodic and more complicated chaotic dynamics. Since we deal with nontrivial recurrences, the size of the neighborhood ¿ to which the trajectory must recur, is larger than zero. This leads to a nonzero width of the lines, which we determine analytically for both periodic and quasiperiodic motion. The understanding of such microscopic structures is important for choosing an appropriate threshold ¿ to analyze experimental data by means of RPs.
AB - In this paper we study recurrence plots (RPs) for the simplest example of nontrivial recurrences, namely in the case of a quasiperiodic motion. This case can be still studied analytically and constitutes a link between simple periodic and more complicated chaotic dynamics. Since we deal with nontrivial recurrences, the size of the neighborhood ¿ to which the trajectory must recur, is larger than zero. This leads to a nonzero width of the lines, which we determine analytically for both periodic and quasiperiodic motion. The understanding of such microscopic structures is important for choosing an appropriate threshold ¿ to analyze experimental data by means of RPs.
KW - recurrence plot
KW - analytic description
KW - quasiperiodic motion
KW - nontrivial recurrence
U2 - 10.1142/S0218127407019949
DO - 10.1142/S0218127407019949
M3 - Article
VL - 17
SP - 4273
EP - 4283
JO - International Journal of Bifurcation and Chaos
JF - International Journal of Bifurcation and Chaos
SN - 0218-1274
IS - 12
ER -