Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica
@article{RUMI_2016_1_1_2_a3, author = {Spigler, Renato}, title = {The mathematics of {Kuramoto} models which describe synchronization phenomena}, journal = {Matematica, cultura e societ\`a}, pages = {123--132}, publisher = {mathdoc}, volume = {Ser. 1, 1}, number = {2}, year = {2016}, zbl = {1404.34066}, mrnumber = {3586455}, language = {en}, url = {http://geodesic.mathdoc.fr/item/RUMI_2016_1_1_2_a3/} }
Spigler, Renato. The mathematics of Kuramoto models which describe synchronization phenomena. Matematica, cultura e società, Série 1, Tome 1 (2016) no. 2, pp. 123-132. http://geodesic.mathdoc.fr/item/RUMI_2016_1_1_2_a3/
[1] Breaking the symmetry in bimodal frequency distributions of globally coupled oscillators", Phys. Rev. E 57, May 1998, 5287-5290. | DOI | MR
, , , and , "[2] Adaptive frequency model for phase-frequency synchronization in large populations of globally coupled nonlinear oscillators", Phys. Rev. Lett. 81, 14 September 1998, 229-2232.
and , "[3] Uncertainty in phasefrequency synchronization of large populations of globally coupled nonlinear oscillators", Phys. D 141, Nos. 1-2, July 2000, 65-79. | DOI | MR
and , "[4] Synchronization in populations of globally coupled oscillators with inertial effects", Phys. Rev. E 62, September 2000, 3437-3454. | DOI | MR
, , and , "[5] Spectral analysis and computation for the Kuramoto-Sakaguchi integroparabolic equation", IMA J. Numer. Anal. 21, no. 1 (2001), 239-263. | DOI | MR | Zbl
, , and , "[6] The Kuramoto model: a simple paradigm for synchronization phenomena", Rev. Modern Phys., 77 (2005), 137-185.
, , , , and , "[7] The TV remote control and beyond: The legacy of Robert Adler", SIAM News, Vol. 40, N. 5, June 2007, pp. 2-3.
and , "[8] Nonlinear integroparabolic equations on unbounded domain: Existence of classical solutions with special properties", Siberian Math. J. 42 (2001), 495-516. | fulltext EuDML | DOI | MR
, , and , "[9] Regularizing a nonlinear integroparabolic Fokker-Planck equation with space-periodic solutions: Existence of strong solutions", Siberian Math. J. 42 (2001), 693-714. | fulltext EuDML | DOI | MR
, , and , "[10] Existence and uniqueness of classical solutions to certain nonlinear integrodifferential Fokker-Planck-type equations", Electron. J. Differential Equations, Vol. 2002 (2002), No. 24, pp. 1-17. | fulltext EuDML | MR | Zbl
, , and , "[11] Uniform and optimal estimates for solutions to singularly perturbed parabolic equations", J. Evol. Equ. 7 (2007), 347-372. | DOI | MR | Zbl
and , "[12] Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators", J. Statist. Phys. 67 (1992), 313-330. | DOI | MR | Zbl
, , and , "[13] Time-periodic phases in populations of nonlinearly coupled oscillators with bimodal frequency distributions", Phys. D, 113 (1998), 79-97. | DOI | MR | Zbl
, , and , "[14] An adaptive model for synchrony in the firefly Pteroptyx malaccae", J. Math. Biol. 29, no. 6 (1991), 571-585. | DOI | MR | Zbl
, "[15] Self-entrainment of a population of coupled non-linear oscillators", International Symposium on Mathematical Problems in Theoretical Physics (Kyoto Univ., Kyoto, 1975), pp. 420-422. Lecture Notes in Phys., 39, Springer, Berlin, 1975. | MR | Zbl
, "[16] Chemical Oscillations, Waves and Turbulence", Springer Series in Synergetics, Springer-Verlag, Berlin, 1984. | DOI | MR | Zbl
, "[17] Existence and uniqueness of solutions to the Kuramoto-Sakaguchi parabolic integrodifferential equation", Differential Integral Equations 13 (2000), 649-667. | MR | Zbl
, and , "[18] Time-independent estimates and a comparison theorem for a nonlinear integroparabolic equation of the Fokker-Planck type", Differential Integral Equations 17 (2004), no. 5-6, 549-570. | MR | Zbl
, and , "[19] Existence, uniqueness, and regularity for the Kuramoto-Sakaguchi equation with unboundedly supported frequency distribution", Differential Integral Equations, 27, No. 9-10 (2014), 879-892. | MR | Zbl
, , and , "[20] Cooperative phenomena in coupled oscillator systems under external fields", Progr. Theor. Phys. 79, 1 (1988), 39-46. | DOI | MR
, "[21] A soluble active rotator model showing phase transitions via mutual entreinment", Progr. Theor. Phys. 76, 3 (1986), 576-581. | DOI | MR
and , "[22] Local and global self-entrainment in oscillator lattices", Progr. Theor. Phys. 77, 5 (1987), 1005-1010.
, , and , "[23] Numerical solution of the Kuramoto-Sakaguchi equation governing populations of coupled oscillators", Math. Models Methods Appl. Sci. 8 (1998), 1023-1038. | DOI | MR | Zbl
, , and , "[24] Stability of incoherence in a population of coupled oscillators", J. Statist. Phys. 63, Nos. 3/4 (1991), 613-635. | DOI | MR
, and , "[25] Selfsynchronization of coupled oscillators with hysteretic responses", Phys. D 100 (1997), 279-300. | Zbl
, , and , "[26] First order phase transition resulting from finite inertia in coupled oscillator systems", Phys. Rev. Lett. 78, N. 11 (1997), 2104-2107.
, , and , "[27] The chemical basis of morphogenesis", Philos. Trans. R. Soc. Lond., Series B, Biologcal Sciences, 237, No. 641 (1952), 37-72. | MR
, "