Synchronization and relaxation for a class of globally coupled Hamiltonian systems

Physica D: Nonlinear Phenomena

Volumn 124, Issue 1-3, 1998, Pages 104-125

  Smereka, Peter ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001582224     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(98)00178-X     Document Type: Article

References (29)

1. Y. Kuramoto, Self-entrainment of a population of coupled nonlinear oscillators in: H. Araki (Ed.), Proceedings of the International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, vol. 39, Springer, New York, 1975, pp. 420-422.
2. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence, Springer, Berlin, New York, 1984.
3. S.H. Strogatz, R.E. Mirollo, P.C. Matthews, Coupled nonlinear oscillators below the synchronization threshold: relaxation by generalized Landau damping, Phys. Rev. Lett. 68 (1992) 2730-2733.
4. L.L. Bonilla, J.C. Neu, R. Spigler, Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators, J. Stat. Phys. 67 (1992) 313-330.
5. S.H. Strogatz, R.E. Mirollo, Phase-locking and critical phenomena in lattices of coupled nonlinear oscillators with random intrinsic frequencies, Physica D 31 (1988) 143-168.
6. K.Y. Sang, R.E. Mirollo, S.H. Strogatz, K. Wiesenfeld, Dynamics of a globally coupled oscillator array, Physica D 48 (1991) 102-112.
7. P.C. Matthews, R.E. Mirollo, S.H. Strogatz, Dynamics of a large system of coupled oscillators, Physica D 52 (1991) 293-331.
8. H. Daido, Generic scaling at the onset of macroscopic mutual entrainment in limit-cycle oscillators with uniform all-to-all coupling Phys. Rev. Lett. 73 (1994) 760-763.
9. J.D. Crawford, Scaling and singularities in the entrainment of globally coupled oscillators, Phys. Rev. Lett. 74 (1995) 4341-4344.
10. H. Daido, Onset of cooperative entrainment in limit-cycle oscillators with uniform all-to-all coupling, Physica D 91 (1996) 24-66.
11. L. Landau, On the vibrations of the electronic plasma, J. Physics (USSR) 10 (1946) 25.
12. O. Penrose, Electrostatic instabilities of a uniform non-Maxwellian plasma, Phys. Fluids 3 (1960) 258-265.
13. G. Russo, P. Smereka, Kinetic theory for bubbly flow I: Collisionless case, SIAM J. Appl. Math. 56 (1996) 327-357.
14. H. Weitzner, Plasma oscillations and Landau damping, Phys. Fluids 6 (1963) 1123-1127.
15. H. Weitzner, Longitudinal Plasma Oscillations, in: H. Grad (Ed.), Magnetic-Fluid and Plasma Dynamics American Mathematical Society, Providence, RI, 1967, pp. 127-150.
16. H. Weitzner, D. Dobrott, Ion Waves in a collisionless plasma, Phys. Fluids 11 (1968) 1123-1127.
17. L. van Wijngaarden, On the equation of motion for mixtures of fluids and gas bubbles, J. Fluid Mech. 33 (1968) 465.
18. R.E. Caflisch, M.J. Miksis, G.C. Papanicolaou, L. Ting, Effective equations for wave propagation in bubbly flow, J. Fluid Mech. 153 (1985) 259.
19. P. Smereka, S. Banerjee The dynamics of periodically driven bubble clouds, Phys. Fluids 31 (1988) 3519.
20. P. Smereka, Effective equations for sound propagation in bubbly fluids, in preparation.
21. J.D. Crawford, Hislop, Application of the method of spectral deformation to the Vlasov-Poisson system, Ann. Phys. 189 (1989) 265-317.
22. M.J. Lighthill, Introduction to Fourier analysis and generalized functions, Cambridge University Press, Cambridge, UK, 1978.
23. D.R. Nicholson, Introduction to Plasma Theory, Wiley, New York, 1982.
24. H. Neunzert, An introduction to the nonlinear Boltzmann-Vlasov equation in Kinetic theory and the Boltzmann equation, Lecture Notes in Mathematics, vol. 1048, 1984, pp. 60-110.
25. W. Braun, K. Hepp, The Vlasov dynamics and its fluctuations in the 1/N limit of interacting classical particles, Commun. Math. Phys. 65 (1977) 101-113.
26. R.L. Pego, M.I. Weinstein, Eigenvalues and instabilities of solitary waves, Phil. Trans. R. Soc. Lond. A 340 (1992) 47.
27. R.L. Pego, M.I. Weinstein, Asymptotic stability of solitary waves, Commun. Math. Phys. 164 (1994) 305-349.
28. R.L. Pego, P. Smereka, M.I. Weinstein, Oscillatory instability of solitary waves in a continuum model of lattice vibrations, Nonlinearity 8 (1995) 921-941.
29. P. Smereka, A Vlasov description of the Euler equation, Nonlinearity 9 (1996) 1361-1386.