12 Phase Reconstruction with Iterated Hilbert Transforms
207
16. H. Kim, R. Eykholt, J. Salas, Nonlinear dynamics, delay times, and embedding windows. Phys.
D 127(1–2), 48–60 (1999)
17. B. Kralemann, L. Cimponeriu, M. Rosenblum, A. Pikovsky, R. Mrowka, Uncovering interaction
of coupled oscillators from data. Phys. Rev. E 76(5 Pt 2), 055201 (2007)
18. B. Kralemann, L. Cimponeriu, M. Rosenblum, A. Pikovsky, R. Mrowka, Phase dynamics of
coupled oscillators reconstructed from data. Phys. Rev. E 77(6), 066205 (2008)
19. B. Kralemann, M. Frühwirth, A. Pikovsky, M. Rosenblum, T. Kenner, J. Schaefer, M. Moser,
In vivo cardiac phase response curve elucidates human respiratory heart rate variability. Nat.
Commun. 4, 2418 (2013)
20. B. Kralemann, A. Pikovsky, M. Rosenblum, Reconstructing phase dynamics of oscillator networks. Chaos 21(2), 025104 (2011)
21. C. Letellier, J. Maquet, L. Le Sceller, G. Gouesbet, L. Aguirre, On the non-equivalence of
observables in phase-space reconstructions from recorded time series. J. Phys. A: Math. Gen.
31(39), 7913 (1998)
22. D. Li, X. Li, Z. Liang, L.J. Voss, J.W. Sleigh, Multiscale permutation entropy analysis of EEG
recordings during sevoflurane anesthesia. J. Neural Eng. 7(4), 046010 (2010)
23. M. Paluš, Multiscale atmospheric dynamics: cross-frequency phase-amplitude coupling in the
air temperature. Phys. Rev. Lett. 112(7), 078702 (2014)
24. M. Paluš, A. Stefanovska, Direction of coupling from phases of interacting oscillators: An
information-theoretic approach. Phys. Rev. E 67, 055201 (2003)
25. Z. Peng, W.T. Peter, F. Chu, An improved Hilbert-Huang transform and its application in
vibration signal analysis. J. Sound Vib. 286(1–2), 187–205 (2005)
26. B. Pietras, A. Daffertshofer, Network dynamics of coupled oscillators and phase reduction
techniques. Phys. Rep. (2019)
27. A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear
Sciences (Cambridge University Press, 2001)
28. T. Rings, K. Lehnertz, Distinguishing between direct and indirect directional couplings in large
oscillator networks: partial or non-partial phase analyses? Chaos: Interdiscip. J. Nonlinear Sci.
26(9), 093106 (2016)
29. M. Rosenblum, L. Cimponeriu, A. Pikovsky, Coupled oscillators approach in analysis of physiological data. Conf. Proc. IEEE Eng. Med. Biol. Soc. 1, 441–4 (2006)
30. M. Rosenblum, A. Pikovsky, Detecting direction of coupling in interacting oscillators. Phys.
Rev. E 64(4), 045202(R) (2001)
31. M. Rosenblum, A. Pikovsky, Synchronization: from pendulum clocks to chaotic lasers and
chemical oscillators. Contemp. Phys. 44(5), 401–416 (2003)
32. T. Sauer, J.A. Yorke, M. Casdagli, Embedology. J. Stat. Phys. 65(3–4), 579–616 (1991)
33. A. Savitzky, M.J. Golay, Smoothing and differentiation of data by simplified least squares
procedures. Anal. Chem. 36(8), 1627–1639 (1964)
34. A. Schlemmer, S. Berg, T. Lilienkamp, S. Luther, U. Parlitz, Spatiotemporal permutation
entropy as a measure for complexity of cardiac arrhythmia. Front. Phys. 6, 39 (2018)
35. T. Stankovski, T. Pereira, P.V.E. McClintock, A. Stefanovska, Coupling functions: universal
insights into dynamical interaction mechanisms. Rev. Mod. Phys. 89, 045001 (2017)
36. T. Stankovski, S. Petkoski, J. Raeder, A.F. Smith, P.V. McClintock, A. Stefanovska, Alterations
in the coupling functions between cortical and cardio-respiratory oscillations due to anaesthesia
with propofol and sevoflurane. Philos. Trans. R. Soc. A: Math., Phys. Eng. Sci. 374(2067),
20150186 (2016)
37. Ç. Topçu, M. Frühwirth, M. Moser, M. Rosenblum, A. Pikovsky, Disentangling respiratory
sinus arrhythmia in heart rate variability records. Physiol. Meas. 39(5), 054002 (2018)
38. A.B. Tort, R. Komorowski, H. Eichenbaum, N. Kopell, Measuring phase-amplitude coupling
between neuronal oscillations of different frequencies. J. Neurophysiol. 104(2), 1195–1210
(2010)
39. A.T. Winfree, The Geometry of Biological Time, vol. 12 (Springer Science & Business Media,
2001)
207
16. H. Kim, R. Eykholt, J. Salas, Nonlinear dynamics, delay times, and embedding windows. Phys.
D 127(1–2), 48–60 (1999)
17. B. Kralemann, L. Cimponeriu, M. Rosenblum, A. Pikovsky, R. Mrowka, Uncovering interaction
of coupled oscillators from data. Phys. Rev. E 76(5 Pt 2), 055201 (2007)
18. B. Kralemann, L. Cimponeriu, M. Rosenblum, A. Pikovsky, R. Mrowka, Phase dynamics of
coupled oscillators reconstructed from data. Phys. Rev. E 77(6), 066205 (2008)
19. B. Kralemann, M. Frühwirth, A. Pikovsky, M. Rosenblum, T. Kenner, J. Schaefer, M. Moser,
In vivo cardiac phase response curve elucidates human respiratory heart rate variability. Nat.
Commun. 4, 2418 (2013)
20. B. Kralemann, A. Pikovsky, M. Rosenblum, Reconstructing phase dynamics of oscillator networks. Chaos 21(2), 025104 (2011)
21. C. Letellier, J. Maquet, L. Le Sceller, G. Gouesbet, L. Aguirre, On the non-equivalence of
observables in phase-space reconstructions from recorded time series. J. Phys. A: Math. Gen.
31(39), 7913 (1998)
22. D. Li, X. Li, Z. Liang, L.J. Voss, J.W. Sleigh, Multiscale permutation entropy analysis of EEG
recordings during sevoflurane anesthesia. J. Neural Eng. 7(4), 046010 (2010)
23. M. Paluš, Multiscale atmospheric dynamics: cross-frequency phase-amplitude coupling in the
air temperature. Phys. Rev. Lett. 112(7), 078702 (2014)
24. M. Paluš, A. Stefanovska, Direction of coupling from phases of interacting oscillators: An
information-theoretic approach. Phys. Rev. E 67, 055201 (2003)
25. Z. Peng, W.T. Peter, F. Chu, An improved Hilbert-Huang transform and its application in
vibration signal analysis. J. Sound Vib. 286(1–2), 187–205 (2005)
26. B. Pietras, A. Daffertshofer, Network dynamics of coupled oscillators and phase reduction
techniques. Phys. Rep. (2019)
27. A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear
Sciences (Cambridge University Press, 2001)
28. T. Rings, K. Lehnertz, Distinguishing between direct and indirect directional couplings in large
oscillator networks: partial or non-partial phase analyses? Chaos: Interdiscip. J. Nonlinear Sci.
26(9), 093106 (2016)
29. M. Rosenblum, L. Cimponeriu, A. Pikovsky, Coupled oscillators approach in analysis of physiological data. Conf. Proc. IEEE Eng. Med. Biol. Soc. 1, 441–4 (2006)
30. M. Rosenblum, A. Pikovsky, Detecting direction of coupling in interacting oscillators. Phys.
Rev. E 64(4), 045202(R) (2001)
31. M. Rosenblum, A. Pikovsky, Synchronization: from pendulum clocks to chaotic lasers and
chemical oscillators. Contemp. Phys. 44(5), 401–416 (2003)
32. T. Sauer, J.A. Yorke, M. Casdagli, Embedology. J. Stat. Phys. 65(3–4), 579–616 (1991)
33. A. Savitzky, M.J. Golay, Smoothing and differentiation of data by simplified least squares
procedures. Anal. Chem. 36(8), 1627–1639 (1964)
34. A. Schlemmer, S. Berg, T. Lilienkamp, S. Luther, U. Parlitz, Spatiotemporal permutation
entropy as a measure for complexity of cardiac arrhythmia. Front. Phys. 6, 39 (2018)
35. T. Stankovski, T. Pereira, P.V.E. McClintock, A. Stefanovska, Coupling functions: universal
insights into dynamical interaction mechanisms. Rev. Mod. Phys. 89, 045001 (2017)
36. T. Stankovski, S. Petkoski, J. Raeder, A.F. Smith, P.V. McClintock, A. Stefanovska, Alterations
in the coupling functions between cortical and cardio-respiratory oscillations due to anaesthesia
with propofol and sevoflurane. Philos. Trans. R. Soc. A: Math., Phys. Eng. Sci. 374(2067),
20150186 (2016)
37. Ç. Topçu, M. Frühwirth, M. Moser, M. Rosenblum, A. Pikovsky, Disentangling respiratory
sinus arrhythmia in heart rate variability records. Physiol. Meas. 39(5), 054002 (2018)
38. A.B. Tort, R. Komorowski, H. Eichenbaum, N. Kopell, Measuring phase-amplitude coupling
between neuronal oscillations of different frequencies. J. Neurophysiol. 104(2), 1195–1210
(2010)
39. A.T. Winfree, The Geometry of Biological Time, vol. 12 (Springer Science & Business Media,
2001)