11 Coupling Functions in Neuroscience
187
25. B. Horwitz, The elusive concept of brain connectivity. Neuroimage 19(2), 466–470 (2003)
26. D. Iatsenko, A. Bernjak, T. Stankovski, Y. Shiogai, P.J. Owen-Lynch, P.B.M. Clarkson, P.V.E.
McClintock, A. Stefanovska, Evolution of cardio-respiratory interactions with age. Phil. Trans.
R. Soc. Lond. A 371(1997), 20110622 (2013)
27. E.M. Izhikevich, Simple model of spiking neurons. IEEE Trans. Neural Netw. 14(6), 1569–
1572 (2003)
28. A. Jafarian, P. Zeidman, V. Litvak, K. Friston, Structure learning in coupled dynamical systems
and dynamic causal modelling. Phil. Trans. R. Soc. A 377, 20190048 (2019)
29. O. Jensen, L.L. Colgin, Cross-frequency coupling between neuronal oscillations. Trends Cognit. Sci. 11(7), 267–269 (2007)
30. V. Jirsa, V. Müller, Cross-frequency coupling in real and virtual brain networks. Front. Comput.
Neurosci. 7, 78 (2013)
31. V. Jurcak, D. Tsuzuki, I. Dan, 10/20, 10/10, and 10/5 systems revisited: their validity as relative
head-surface-based positioning systems. Neuroimage 34(4), 1600–1611 (2007)
32. I.Z. Kiss, C.G. Rusin, H. Kori, J.L. Hudson, Engineering complex dynamical structures: sequential patterns and desynchronization. Science 316(5833), 1886–1889 (2007)
33. I.Z. Kiss, Y. Zhai, J.L. Hudson, Predicting mutual entrainment of oscillators with experimentbased phase models. Phys. Rev. Lett. 94, 248301 (2005)
34. B. Kralemann, L. Cimponeriu, M. Rosenblum, A. Pikovsky, R. Mrowka, Phase dynamics of
coupled oscillators reconstructed from data. Phys. Rev. E 77(6, Part 2), 066205 (2008)
35. 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)
36. Y. Kuramoto, Self-entrainment of a population of coupled non-linear oscillators, in Lecture
Notes in Physics, vol. 39, ed. by H. Araki (Springer, New York, 1975), pp. 420–422
37. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984)
38. G. Lancaster, D. Iatsenko, A. Pidde, V. Ticcinelli, A. Stefanovska, Surrogate data for hypothesis
testing of physical systems. Phys. Rep. (2018)
39. Z. Levnaji´ c, A. Pikovsky, Network reconstruction from random phase resetting. Phys. Rev.
Lett. 107, 034101 (2011). https://doi.org/10.1103/PhysRevLett.107.034101
40. D. Lukarski, M. Ginovska, H. Spasevska, T. Stankovski, Time window determination for inference of time-varying dynamics: application to cardiorespiratory interaction. Front. Physiol. 11
(2020)
41. W. Moon, J.S. Wettlaufer, Coupling functions in climate. Phil. Trans. R. Soc. A 377(2160),
20190006 (2019)
42. C. Morris, H. Lecar, Voltage oscillations in the barnacle giant muscle fiber. Biophys. J. 35(1),
193–213 (1981)
43. B. Musizza, A. Stefanovska, P.V.E. McClintock, M. Paluš, J. Petrovˇ ciˇ c, S. Ribariˇ c, F.F. Bajrovi´ c,
Interactions between cardiac, respiratory, and EEG-δ oscillations in rats during anæsthesia. J.
Physiol. (London) 580(1), 315–326 (2007)
44. G. Nadzinski, M. Dobrevski, C. Anderson, P.V.E. McClintock, A. Stefanovska, M. Stankovski,
T. Stankovski, Experimental realization of the coupling function secure communications protocol and analysis of its noise robustness. IEEE Trans. Info. Forens. Secur. 13(10), 2591–2601
(2018)
45. H. Nakao, Phase reduction approach to synchronisation of nonlinear oscillators. Contem. Phys.
57(2), 188–214 (2016)
46. E. Niedermeyer, F.L. da Silva, Electroencephalography: Basic Principles, Clinical Applications, and Related Fields (Lippincott Williams & Wilkins, 2005)
47. T. Onojima, T. Goto, H. Mizuhara, T. Aoyagi, A dynamical systems approach for estimating
phase interactions between rhythms of different frequencies from experimental data. PLoS
Comput. Biol. 14(1), e1005928 (2018)
48. S.A. Oprisan, A.A. Prinz, C.C. Canavier, Phase resetting and phase locking in hybrid circuits
of one model and one biological neuron. Biophys. J. 87(4), 2283–2298 (2004)
187
25. B. Horwitz, The elusive concept of brain connectivity. Neuroimage 19(2), 466–470 (2003)
26. D. Iatsenko, A. Bernjak, T. Stankovski, Y. Shiogai, P.J. Owen-Lynch, P.B.M. Clarkson, P.V.E.
McClintock, A. Stefanovska, Evolution of cardio-respiratory interactions with age. Phil. Trans.
R. Soc. Lond. A 371(1997), 20110622 (2013)
27. E.M. Izhikevich, Simple model of spiking neurons. IEEE Trans. Neural Netw. 14(6), 1569–
1572 (2003)
28. A. Jafarian, P. Zeidman, V. Litvak, K. Friston, Structure learning in coupled dynamical systems
and dynamic causal modelling. Phil. Trans. R. Soc. A 377, 20190048 (2019)
29. O. Jensen, L.L. Colgin, Cross-frequency coupling between neuronal oscillations. Trends Cognit. Sci. 11(7), 267–269 (2007)
30. V. Jirsa, V. Müller, Cross-frequency coupling in real and virtual brain networks. Front. Comput.
Neurosci. 7, 78 (2013)
31. V. Jurcak, D. Tsuzuki, I. Dan, 10/20, 10/10, and 10/5 systems revisited: their validity as relative
head-surface-based positioning systems. Neuroimage 34(4), 1600–1611 (2007)
32. I.Z. Kiss, C.G. Rusin, H. Kori, J.L. Hudson, Engineering complex dynamical structures: sequential patterns and desynchronization. Science 316(5833), 1886–1889 (2007)
33. I.Z. Kiss, Y. Zhai, J.L. Hudson, Predicting mutual entrainment of oscillators with experimentbased phase models. Phys. Rev. Lett. 94, 248301 (2005)
34. B. Kralemann, L. Cimponeriu, M. Rosenblum, A. Pikovsky, R. Mrowka, Phase dynamics of
coupled oscillators reconstructed from data. Phys. Rev. E 77(6, Part 2), 066205 (2008)
35. 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)
36. Y. Kuramoto, Self-entrainment of a population of coupled non-linear oscillators, in Lecture
Notes in Physics, vol. 39, ed. by H. Araki (Springer, New York, 1975), pp. 420–422
37. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984)
38. G. Lancaster, D. Iatsenko, A. Pidde, V. Ticcinelli, A. Stefanovska, Surrogate data for hypothesis
testing of physical systems. Phys. Rep. (2018)
39. Z. Levnaji´ c, A. Pikovsky, Network reconstruction from random phase resetting. Phys. Rev.
Lett. 107, 034101 (2011). https://doi.org/10.1103/PhysRevLett.107.034101
40. D. Lukarski, M. Ginovska, H. Spasevska, T. Stankovski, Time window determination for inference of time-varying dynamics: application to cardiorespiratory interaction. Front. Physiol. 11
(2020)
41. W. Moon, J.S. Wettlaufer, Coupling functions in climate. Phil. Trans. R. Soc. A 377(2160),
20190006 (2019)
42. C. Morris, H. Lecar, Voltage oscillations in the barnacle giant muscle fiber. Biophys. J. 35(1),
193–213 (1981)
43. B. Musizza, A. Stefanovska, P.V.E. McClintock, M. Paluš, J. Petrovˇ ciˇ c, S. Ribariˇ c, F.F. Bajrovi´ c,
Interactions between cardiac, respiratory, and EEG-δ oscillations in rats during anæsthesia. J.
Physiol. (London) 580(1), 315–326 (2007)
44. G. Nadzinski, M. Dobrevski, C. Anderson, P.V.E. McClintock, A. Stefanovska, M. Stankovski,
T. Stankovski, Experimental realization of the coupling function secure communications protocol and analysis of its noise robustness. IEEE Trans. Info. Forens. Secur. 13(10), 2591–2601
(2018)
45. H. Nakao, Phase reduction approach to synchronisation of nonlinear oscillators. Contem. Phys.
57(2), 188–214 (2016)
46. E. Niedermeyer, F.L. da Silva, Electroencephalography: Basic Principles, Clinical Applications, and Related Fields (Lippincott Williams & Wilkins, 2005)
47. T. Onojima, T. Goto, H. Mizuhara, T. Aoyagi, A dynamical systems approach for estimating
phase interactions between rhythms of different frequencies from experimental data. PLoS
Comput. Biol. 14(1), e1005928 (2018)
48. S.A. Oprisan, A.A. Prinz, C.C. Canavier, Phase resetting and phase locking in hybrid circuits
of one model and one biological neuron. Biophys. J. 87(4), 2283–2298 (2004)