6 Synchronisation and Non-autonomicity
109
17. M. Ghil, M.D. Chekroun, E. Simonnet, Climate dynamics and fluid mechanics: natural variability and related uncertainties. Phys. D 237(14–17), 2111–2126 (2008)
18. Z. Hagos, T. Stankovski, J. Newman, T. Pereira, P.V. McClintock, A. Stefanovska, Synchronization transitions caused by time-varying coupling functions. Philos. Trans. R Soc. A 377(2160),
20190275 (2019)
19. P. Holme, Modern temporal network theory: a colloquium. Eur. Phys. J B 88(9), 234 (2015)
20. P. Holme, J. Saramäki, Temporal networks. Phys. Rep. 519(3), 97–125 (2012)
21. A. Iggidr, G. Sallet, On the stability of nonautonomous systems. Automatica 39(1), 167–171
(2003)
22. R.V. Jensen, Synchronization of driven nonlinear oscillators. Am. J. Phys. 70(6), 607–619
(2002)
23. C. Kim, E.K. Lee, P. Talkner, Numerical method for solving stochastic differential equations
with dichotomous noise. Phys. Rev. E 73(2), 026101 (2006)
24. P.E. Kloeden, C. Pötzsche, Nonautonomous dynamical systems in the life sciences, in Nonautonomous Dynamical Systems in the Life Sciences (Springer, 2013), pp. 3–39
25. P.E. Kloeden, M. Rasmussen, Nonautonomous Dynamical Systems (American Mathematical
Society, Providence, 2011)
26. Y. Kuramoto, Self-entrainment of a population of coupled non-linear oscillators title, in International Symposium on Mathematical Problems in Theoretical Physics, Kyoto (1975), pp.
420–422
27. W. Kurebayashi, S. Shirasaka, H. Nakao, Phase reduction method for strongly perturbed limit
cycle oscillators. Phys. Rev. Lett. 111(21), 214101 (2013)
28. W. Kurebayashi, S. Shirasaka, H. Nakao, A criterion for timescale decomposition of external
inputs for generalized phase reduction of limit-cycle oscillators. NOLTA 6(2), 171–180 (2015)
29. G. Lancaster, P.T. Clemson, Y.F. Suprunenko, T. Stankovski, A. Stefanovska, Detecting chronotaxic systems from single-variable time series with separable amplitude and phase. Entropy
17(6), 4413–4438 (2015)
30. G. Lancaster, Y.F. Suprunenko, K. Jenkins, A. Stefanovska, Modelling chronotaxicity of cellular energy metabolism to facilitate the identification of altered metabolic states. Sci. Rep. 6,
29584 (2016)
31. J.A. Langa, J.C. Robinson, A. Suárez, Stability, instability, and bifurcation phenomena in nonautonomous differential equations. Nonlinearity 15(3), 887 (2002)
32. J.P. LaSalle, Stability of nonautonomous systems. Technical Report, Brown Univ. Providence
Ri Lefschetz Center for Dynamical Systems (1976)
33. M. Lucas, D. Fanelli, T. Carletti, J. Petit, Desynchronization induced by time-varying network.
EPL 121(5), 50008 (2018)
34. M. Lucas, D. Fanelli, A. Stefanovska, Nonautonomous driving induces stability in network of
identical oscillators. Phys. Rev. E 99(1), 012309 (2019)
35. M. Lucas, J. Newman, A. Stefanovska, Stabilization of dynamics of oscillatory systems by
nonautonomous perturbation. Phys. Rev. E 97(4), 042209 (2018)
36. D.J. Lurie, D. Kessler, D.S. Bassett, R.F. Betzel, M. Breakspear, S. Kheilholz, A. Kucyi, R.
Liégeois, M.A. Lindquist, A.R. McIntosh et al., Questions and controversies in the study of
time-varying functional connectivity in resting fMRI. Netw. Neurosci. 4(1), 30–69 (2020)
37. D. Malicet, Random walks on Homeo(S 1 ). Commun. Math. Phys. 356(3), 1083–1116 (2017)
38. D.R. Merkin, The stability of nonautonomous systems, in Introduction to the Theory of Stability
(Springer, 1997)
39. J. Newman, Necessary and sufficient conditions for stable synchronization in random dynamical
systems. Ergod. Theory Dyn. Syst. 1–19 (2017)
40. J. Newman, M. Lucas, A. Stefanovska, Non-asymptotic-time Dynamics. In: Physics of Biological Oscillators (Springer, Berlin, 2020)
41. V.I. Oseledets, A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems. Tr. Mosk. Mat. Obs. 19, 179–210 (1968)
42. W. Ott, J.A. Yorke, When Lyapunov exponents fail to exist. Phys. Rev. E 78(5), 056203 (2008)
109
17. M. Ghil, M.D. Chekroun, E. Simonnet, Climate dynamics and fluid mechanics: natural variability and related uncertainties. Phys. D 237(14–17), 2111–2126 (2008)
18. Z. Hagos, T. Stankovski, J. Newman, T. Pereira, P.V. McClintock, A. Stefanovska, Synchronization transitions caused by time-varying coupling functions. Philos. Trans. R Soc. A 377(2160),
20190275 (2019)
19. P. Holme, Modern temporal network theory: a colloquium. Eur. Phys. J B 88(9), 234 (2015)
20. P. Holme, J. Saramäki, Temporal networks. Phys. Rep. 519(3), 97–125 (2012)
21. A. Iggidr, G. Sallet, On the stability of nonautonomous systems. Automatica 39(1), 167–171
(2003)
22. R.V. Jensen, Synchronization of driven nonlinear oscillators. Am. J. Phys. 70(6), 607–619
(2002)
23. C. Kim, E.K. Lee, P. Talkner, Numerical method for solving stochastic differential equations
with dichotomous noise. Phys. Rev. E 73(2), 026101 (2006)
24. P.E. Kloeden, C. Pötzsche, Nonautonomous dynamical systems in the life sciences, in Nonautonomous Dynamical Systems in the Life Sciences (Springer, 2013), pp. 3–39
25. P.E. Kloeden, M. Rasmussen, Nonautonomous Dynamical Systems (American Mathematical
Society, Providence, 2011)
26. Y. Kuramoto, Self-entrainment of a population of coupled non-linear oscillators title, in International Symposium on Mathematical Problems in Theoretical Physics, Kyoto (1975), pp.
420–422
27. W. Kurebayashi, S. Shirasaka, H. Nakao, Phase reduction method for strongly perturbed limit
cycle oscillators. Phys. Rev. Lett. 111(21), 214101 (2013)
28. W. Kurebayashi, S. Shirasaka, H. Nakao, A criterion for timescale decomposition of external
inputs for generalized phase reduction of limit-cycle oscillators. NOLTA 6(2), 171–180 (2015)
29. G. Lancaster, P.T. Clemson, Y.F. Suprunenko, T. Stankovski, A. Stefanovska, Detecting chronotaxic systems from single-variable time series with separable amplitude and phase. Entropy
17(6), 4413–4438 (2015)
30. G. Lancaster, Y.F. Suprunenko, K. Jenkins, A. Stefanovska, Modelling chronotaxicity of cellular energy metabolism to facilitate the identification of altered metabolic states. Sci. Rep. 6,
29584 (2016)
31. J.A. Langa, J.C. Robinson, A. Suárez, Stability, instability, and bifurcation phenomena in nonautonomous differential equations. Nonlinearity 15(3), 887 (2002)
32. J.P. LaSalle, Stability of nonautonomous systems. Technical Report, Brown Univ. Providence
Ri Lefschetz Center for Dynamical Systems (1976)
33. M. Lucas, D. Fanelli, T. Carletti, J. Petit, Desynchronization induced by time-varying network.
EPL 121(5), 50008 (2018)
34. M. Lucas, D. Fanelli, A. Stefanovska, Nonautonomous driving induces stability in network of
identical oscillators. Phys. Rev. E 99(1), 012309 (2019)
35. M. Lucas, J. Newman, A. Stefanovska, Stabilization of dynamics of oscillatory systems by
nonautonomous perturbation. Phys. Rev. E 97(4), 042209 (2018)
36. D.J. Lurie, D. Kessler, D.S. Bassett, R.F. Betzel, M. Breakspear, S. Kheilholz, A. Kucyi, R.
Liégeois, M.A. Lindquist, A.R. McIntosh et al., Questions and controversies in the study of
time-varying functional connectivity in resting fMRI. Netw. Neurosci. 4(1), 30–69 (2020)
37. D. Malicet, Random walks on Homeo(S 1 ). Commun. Math. Phys. 356(3), 1083–1116 (2017)
38. D.R. Merkin, The stability of nonautonomous systems, in Introduction to the Theory of Stability
(Springer, 1997)
39. J. Newman, Necessary and sufficient conditions for stable synchronization in random dynamical
systems. Ergod. Theory Dyn. Syst. 1–19 (2017)
40. J. Newman, M. Lucas, A. Stefanovska, Non-asymptotic-time Dynamics. In: Physics of Biological Oscillators (Springer, Berlin, 2020)
41. V.I. Oseledets, A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems. Tr. Mosk. Mat. Obs. 19, 179–210 (1968)
42. W. Ott, J.A. Yorke, When Lyapunov exponents fail to exist. Phys. Rev. E 78(5), 056203 (2008)