2 Phase and Amplitude Description of Complex Oscillatory Patterns …
27
27. B. Pietras, A. Daffertshofer, Network dynamics of coupled oscillators and phase reduction
techniques. Phys. Rep. 819, 1–105 (2019)
28. A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear
Sciences (Cambridge University Press, Cambridge, 2001)
29. M. Rosenblum, A. Pikovsky, Numerical phase reduction beyond the first order approximation.
Chaos 29, 011105 (2019)
30. S. Shirasaka, W. Kurebayashi, H. Nakao, Phase-amplitude reduction of transient dynamics far
from attractors for limit-cycling systems. Chaos 27, 023119 (2017)
31. T. Stankovski, T. Pereira, P.V.E. McClintock, A. Stefanovska, Coupling functions: universal
insights into dynamical interaction mechanisms. Rev. Mod. Phys. 89, 045001 (2017)
32. S. Strogatz, Sync: The Emerging Science of Spontaneous Order (Penguin Books, London,
2004)
33. K. Taira, H. Nakao, Phase-response analysis of synchronization for periodic flows. J. Fluid
Mech. 846, R2 (2018)
34. P.A. Tass, Phase Resetting in Medicine and Biology: Stochastic Modeling and Data Analysis
(Springer, Berlin, 2007)
35. K.C.A. Wedgwood, K.K. Lin, R. Thul, S. Coombes, Phase-amplitude descriptions of neural
oscillator models. J. Math. Neurosci. 3, 2 (2013)
36. D. Wilson, Phase-amplitude reduction far beyond the weakly perturbed paradigm. Phys. Rev.
E 101, 022220 (2020)
37. D. Wilson, B. Ermentrout, Phase models beyond weak coupling. Phys. Rev. Lett. 123, 164101
(2019)
38. D. Wilson, J. Moehlis, Isostable reduction of periodic orbits. Phys. Rev. E 94, 052213 (2016)
39. A.T. Winfree, The Geometry of Biological Time (Springer, New York, 2001)
40. A. Zlotnik, Y. Chen, I.Z. Kiss, H.-A. Tanaka, J.-S. Li, Optimal waveform for fast entrainment
of weakly forced nonlinear oscillators. Phys. Rev. Lett. 111, 024102 (2013)
27
27. B. Pietras, A. Daffertshofer, Network dynamics of coupled oscillators and phase reduction
techniques. Phys. Rep. 819, 1–105 (2019)
28. A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear
Sciences (Cambridge University Press, Cambridge, 2001)
29. M. Rosenblum, A. Pikovsky, Numerical phase reduction beyond the first order approximation.
Chaos 29, 011105 (2019)
30. S. Shirasaka, W. Kurebayashi, H. Nakao, Phase-amplitude reduction of transient dynamics far
from attractors for limit-cycling systems. Chaos 27, 023119 (2017)
31. T. Stankovski, T. Pereira, P.V.E. McClintock, A. Stefanovska, Coupling functions: universal
insights into dynamical interaction mechanisms. Rev. Mod. Phys. 89, 045001 (2017)
32. S. Strogatz, Sync: The Emerging Science of Spontaneous Order (Penguin Books, London,
2004)
33. K. Taira, H. Nakao, Phase-response analysis of synchronization for periodic flows. J. Fluid
Mech. 846, R2 (2018)
34. P.A. Tass, Phase Resetting in Medicine and Biology: Stochastic Modeling and Data Analysis
(Springer, Berlin, 2007)
35. K.C.A. Wedgwood, K.K. Lin, R. Thul, S. Coombes, Phase-amplitude descriptions of neural
oscillator models. J. Math. Neurosci. 3, 2 (2013)
36. D. Wilson, Phase-amplitude reduction far beyond the weakly perturbed paradigm. Phys. Rev.
E 101, 022220 (2020)
37. D. Wilson, B. Ermentrout, Phase models beyond weak coupling. Phys. Rev. Lett. 123, 164101
(2019)
38. D. Wilson, J. Moehlis, Isostable reduction of periodic orbits. Phys. Rev. E 94, 052213 (2016)
39. A.T. Winfree, The Geometry of Biological Time (Springer, New York, 2001)
40. A. Zlotnik, Y. Chen, I.Z. Kiss, H.-A. Tanaka, J.-S. Li, Optimal waveform for fast entrainment
of weakly forced nonlinear oscillators. Phys. Rev. Lett. 111, 024102 (2013)