128
J. M. I. Newman et al.
14. R.V. Jensen, Synchronization of driven nonlinear oscillators. Am. J. Phys. 70(6), 607–619
(2002)
15. D. Karrasch, Linearization of hyperbolic finite-time processes. J. Differ. Equ. 254(1), 256–282
(2013)
16. B. Kaszás, U. Feudel, T. Tél, Leaking in history space: a way to analyze systems subjected to
arbitrary driving. Chaos 28(3), 033,612 (2018)
17. A. Katok, B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Encyclopedia of Mathematics and its Applications (Cambridge University Press, Cambridge, 1995)
18. P.E. Kloeden, M. Rasmussen, Nonautonomous Dynamical Systems (American Mathematical
Society, Providence, 2011)
19. C. Kuehn, Multiple Time Scale Dynamics, Applied Mathematical Sciences, vol. 191 (Springer,
Cham, 2015)
20. Y. Lehahn, F. d’Ovidio, M. Lévy, E. Heifetz, Stirring of the northeast Atlantic spring bloom:
A Lagrangian analysis based on multisatellite data. J. Geophys. Res. C 112(C8) (2007)
21. F. Lekien, S.C. Shadden, J.E. Marsden, Lagrangian coherent structures in n-dimensional systems. J. Math. Phys. 48(6), 065,404 (2007)
22. M. Lucas, D. Fanelli, A. Stefanovska, Nonautonomous driving induces stability in network of
identical oscillators. Phys. Rev. E 99(1), 012,309 (2019)
23. M. Lucas, J. Newman, A. Stefanovska, Stabilization of dynamics of oscillatory systems by
nonautonomous perturbation. Phys. Rev. E 97(4), 042,209 (2018)
24. M. Lucas, J.M.I. Newman, A. Stefanovska, Synchronisation and non-autonomicity. In: Stefanovska A., McClintock P.V.E. (eds) Physics of Biological Oscillators. Understanding Complex Systems, pp. 85–110, (Springer, Cham, 2021). https://doi.org/10.1007/978-3-030-598051_6
25. A.M. Lyapunov, The general problem of the stability of motion. Int. J. Control 55(3), 531–534
(1992)
26. R.L. Moorcroft, S.M. Fielding, Criteria for shear banding in time-dependent flows of complex
fluids. Phys. Rev. Lett. 110(8), 086,001 (2013)
27. J. Newman, M. Lucas, A. Stefanovska, Stabilisation of cyclic processes by slowly varying
forcing (2019). Submitted
28. A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear
Sciences, vol. 12 (Cambridge University Press, Cambridge, UK, 2003)
29. H. Poincaré, Mémoire sur les courbes définies par une équation différentielle (J. Math, Pures
Appl, 1881)
30. A.G. Ramos et al., Lagrangian coherent structure assisted path planning for transoceanic
autonomous underwater vehicle missions. Sci. Rep. 8, 4575 (2018)
31. M. Rasmussen, Finite-time attractivity and bifurcation for nonautonomous differential equations. Differ. Equ. Dynam. Syst. 18(1), 57–78 (2010)
32. S.C. Shadden, J.O. Dabiri, J.E. Marsden, Lagrangian analysis of fluid transport in empirical
vortex ring flows. Phys. Fluids 18(4), 047,105 (2006)
33. A. Stefanovska, P.T. Clemson, Y.F. Suprunenko, Introduction to chronotaxic systems – systems far from thermodynamics equilibrium that adjust their clocks. In: Wunner G., Pelster
A. (eds) Selforganization in Complex Systems: the Past, Present, and Future of Synergetics.
Understanding Complex Systems, pp. 227–246, (Springer, Cham, 2016). https://doi.org/10.
1007/978-3-319-27635-9_14
34. S.H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, 2nd edn. (Westview Press, Boulder, 2014)
35. E. Tew Kai, V. Rossi, J. Sudre, H. Weimerskirch, C. Lopez, E. Hernandez-Garcia, F. Marsac, V.
Garçon, Top marine predators track Lagrangian coherent structures. PNAS 106(20), 8245–8250
(2009)
36. J. Töger, M. Kanski, M. Carlsson, S.J. Kovács, G. Söderlind, H. Arheden, E. Heiberg, Vortex
ring formation in the left ventricle of the heart: analysis by 4D flow MRI and Lagrangian
coherent structures. Ann. Biomed. Eng. 40(12), 2652–2662 (2012)
J. M. I. Newman et al.
14. R.V. Jensen, Synchronization of driven nonlinear oscillators. Am. J. Phys. 70(6), 607–619
(2002)
15. D. Karrasch, Linearization of hyperbolic finite-time processes. J. Differ. Equ. 254(1), 256–282
(2013)
16. B. Kaszás, U. Feudel, T. Tél, Leaking in history space: a way to analyze systems subjected to
arbitrary driving. Chaos 28(3), 033,612 (2018)
17. A. Katok, B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Encyclopedia of Mathematics and its Applications (Cambridge University Press, Cambridge, 1995)
18. P.E. Kloeden, M. Rasmussen, Nonautonomous Dynamical Systems (American Mathematical
Society, Providence, 2011)
19. C. Kuehn, Multiple Time Scale Dynamics, Applied Mathematical Sciences, vol. 191 (Springer,
Cham, 2015)
20. Y. Lehahn, F. d’Ovidio, M. Lévy, E. Heifetz, Stirring of the northeast Atlantic spring bloom:
A Lagrangian analysis based on multisatellite data. J. Geophys. Res. C 112(C8) (2007)
21. F. Lekien, S.C. Shadden, J.E. Marsden, Lagrangian coherent structures in n-dimensional systems. J. Math. Phys. 48(6), 065,404 (2007)
22. M. Lucas, D. Fanelli, A. Stefanovska, Nonautonomous driving induces stability in network of
identical oscillators. Phys. Rev. E 99(1), 012,309 (2019)
23. M. Lucas, J. Newman, A. Stefanovska, Stabilization of dynamics of oscillatory systems by
nonautonomous perturbation. Phys. Rev. E 97(4), 042,209 (2018)
24. M. Lucas, J.M.I. Newman, A. Stefanovska, Synchronisation and non-autonomicity. In: Stefanovska A., McClintock P.V.E. (eds) Physics of Biological Oscillators. Understanding Complex Systems, pp. 85–110, (Springer, Cham, 2021). https://doi.org/10.1007/978-3-030-598051_6
25. A.M. Lyapunov, The general problem of the stability of motion. Int. J. Control 55(3), 531–534
(1992)
26. R.L. Moorcroft, S.M. Fielding, Criteria for shear banding in time-dependent flows of complex
fluids. Phys. Rev. Lett. 110(8), 086,001 (2013)
27. J. Newman, M. Lucas, A. Stefanovska, Stabilisation of cyclic processes by slowly varying
forcing (2019). Submitted
28. A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear
Sciences, vol. 12 (Cambridge University Press, Cambridge, UK, 2003)
29. H. Poincaré, Mémoire sur les courbes définies par une équation différentielle (J. Math, Pures
Appl, 1881)
30. A.G. Ramos et al., Lagrangian coherent structure assisted path planning for transoceanic
autonomous underwater vehicle missions. Sci. Rep. 8, 4575 (2018)
31. M. Rasmussen, Finite-time attractivity and bifurcation for nonautonomous differential equations. Differ. Equ. Dynam. Syst. 18(1), 57–78 (2010)
32. S.C. Shadden, J.O. Dabiri, J.E. Marsden, Lagrangian analysis of fluid transport in empirical
vortex ring flows. Phys. Fluids 18(4), 047,105 (2006)
33. A. Stefanovska, P.T. Clemson, Y.F. Suprunenko, Introduction to chronotaxic systems – systems far from thermodynamics equilibrium that adjust their clocks. In: Wunner G., Pelster
A. (eds) Selforganization in Complex Systems: the Past, Present, and Future of Synergetics.
Understanding Complex Systems, pp. 227–246, (Springer, Cham, 2016). https://doi.org/10.
1007/978-3-319-27635-9_14
34. S.H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, 2nd edn. (Westview Press, Boulder, 2014)
35. E. Tew Kai, V. Rossi, J. Sudre, H. Weimerskirch, C. Lopez, E. Hernandez-Garcia, F. Marsac, V.
Garçon, Top marine predators track Lagrangian coherent structures. PNAS 106(20), 8245–8250
(2009)
36. J. Töger, M. Kanski, M. Carlsson, S.J. Kovács, G. Söderlind, H. Arheden, E. Heiberg, Vortex
ring formation in the left ventricle of the heart: analysis by 4D flow MRI and Lagrangian
coherent structures. Ann. Biomed. Eng. 40(12), 2652–2662 (2012)