-
1
-
-
19944385353
-
The Kuramoto model: A simple paradigm for synchronization phenomena
-
DOI 10.1103/RevModPhys.77.137
-
ACEBRÓN, J. A., BONILLA, L. L., PÉREZ VICENTE, C. J., RITORT, F. and SPIGLER, R. (2005). The Kuramoto model: A simple paradigm for synchronization phenomena. Rev. Modern Phys. 77 137-185. (Pubitemid 41490657)
-
(2005)
Reviews of Modern Physics
, vol.77
, Issue.1
, pp. 137-185
-
-
Acebron, J.A.1
Bonilla, L.L.2
Vicente, C.J.P.3
Ritort, F.4
Spigler, R.5
-
2
-
-
84861896478
-
Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons
-
BALADRON, J., FASOLI, D., FAUGERAS, O. and TOUBOUL, J. (2012). Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons. J. Math. Neurosci. 2 Art. 10, 50.
-
(2012)
J. Math. Neurosci. 2 Art.
, vol.10
, pp. 50
-
-
Baladron, J.1
Fasoli, D.2
Faugeras, O.3
Touboul, J.4
-
4
-
-
77956719419
-
Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation
-
BOLLEY, F., GUILLIN, A. and MALRIEU, F. (2010). Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation. M2AN Math. Model. Numer. Anal. 44 867-884.
-
(2010)
M2AN Math. Model. Numer. Anal.
, vol.44
, pp. 867-884
-
-
Bolley, F.1
Guillin, A.2
Malrieu, F.3
-
5
-
-
33845889473
-
Quantitative concentration inequalities for empirical measures on non-compact spaces
-
BOLLEY, F.,GUILLIN, A. andVILLANI, C. (2007). Quantitative concentration inequalities for empirical measures on non-compact spaces. Probab. Theory Related Fields 137 541-593.
-
(2007)
Probab. Theory Related Fields
, vol.137
, pp. 541-593
-
-
Bolley F.Guillin, A.1
Villani, C.2
-
7
-
-
0030489571
-
Convergence rate for the approximation of the limit law of weakly interacting particles: Application to the Burgers equation
-
BOSSY, M. and TALAY, D. (1996). Convergence rate for the approximation of the limit law of weakly interacting particles: Application to the Burgers equation. Ann. Appl. Probab. 6 818-861.
-
(1996)
Ann. Appl. Probab.
, vol.6
, pp. 818-861
-
-
Bossy, M.1
Talay, D.2
-
8
-
-
0003196688
-
Second order PDE's in finite and infinite dimension: A probabilistic approach
-
Springer, Berlin
-
CERRAI, S. (2001). Second Order PDE's in Finite and Infinite Dimension: A Probabilistic Approach. Lecture Notes in Math. 1762. Springer, Berlin.
-
(2001)
Lecture Notes in Math.
, vol.1762
-
-
Cerrai, S.1
-
9
-
-
77954517934
-
Synchronization of oscillators with long-range power law interactions
-
CHOWDHURY, D. and CROSS, M. C. (2010). Synchronization of oscillators with long-range power law interactions. Phys. Rev. E, 82 016205.
-
(2010)
Phys. Rev. E
, vol.82
, pp. 016205
-
-
Chowdhury, D.1
Cross, M.C.2
-
10
-
-
0030210666
-
McKean-Vlasov limit for interacting random processes in random media
-
DAI PRA, P. and DEN HOLLANDER, F. (1996). McKean-Vlasov limit for interacting random processes in random media. J. Stat. Phys. 84 735-772.
-
(1996)
J. Stat. Phys.
, vol.84
, pp. 735-772
-
-
Dai Pra, P.1
Den Hollander, F.2
-
11
-
-
0032339667
-
Some remarks about backward itô formula and applications
-
DA PRATO, G. and TUBARO, L. (1998). Some remarks about backward Itô formula and applications. Stoch. Anal. Appl. 16 993-1003. (Pubitemid 128375632)
-
(1998)
Stochastic Analysis and Applications
, vol.16
, Issue.6
, pp. 993-1003
-
-
Da Prato, G.1
Tubaro, L.2
-
12
-
-
84888422811
-
-
Available at arXiv: 1211.0299
-
DELARUE, F., INGLIS, J., RUBENTHALER, S. and TANRÉ, E. (2012). Global solvability of a networked integrate-and-fire model of McKean-Vlasov type. Available at arXiv:1211.0299.
-
(2012)
Global solvability of a networked integrate-and-fire model of McKean-Vlasov type
-
-
Delarue, F.1
Inglis, J.2
Rubenthaler, S.3
Tanré, E.4
-
13
-
-
0007461162
-
A moran particle system approximation of feynman- kac formulae
-
DEL MORAL, P. andMICLO, L. (2000). A Moran particle system approximation of Feynman- Kac formulae. Stochastic Process. Appl. 86 193-216.
-
(2000)
Stochastic Process. Appl.
, vol.86
, pp. 193-216
-
-
Del Moral, P.1
Miclo, L.2
-
16
-
-
84985400388
-
On the McKean-Vlasov limit for interacting diffusions
-
GÄRTNER, J. (1988). On the McKean-Vlasov limit for interacting diffusions. Math. Nachr. 137 197-248.
-
(1988)
Math. Nachr.
, vol.137
, pp. 197-248
-
-
Gärtner, J.1
-
19
-
-
84859795069
-
Global attractor and asymptotic dynamics in the Kuramoto model for coupled noisy phase oscillators
-
GIACOMIN, G., PAKDAMAN, K. and PELLEGRIN, X. (2012). Global attractor and asymptotic dynamics in the Kuramoto model for coupled noisy phase oscillators. Nonlinearity 25 1247-1273.
-
(2012)
Nonlinearity
, vol.25
, pp. 1247-1273
-
-
Giacomin, G.1
Pakdaman, K.2
Pellegrin, X.3
-
20
-
-
84862156782
-
One-dimensional lattice of oscillators coupled through power-law interactions: Continuum limit and dynamics of spatial Fourier modes
-
GUPTA, S., POTTERS, M. and RUFFO, S. (2012). One-dimensional lattice of oscillators coupled through power-law interactions: Continuum limit and dynamics of spatial Fourier modes. Phys. Rev. E, 85 066201.
-
(2012)
Phys. Rev. E
, vol.85
, pp. 066201
-
-
Gupta, S.1
Potters, M.2
Ruffo, S.3
-
22
-
-
0032325532
-
Propagation of chaos and fluctuations for a moderate model with smooth initial data
-
JOURDAIN, B. andMÉLÉARD, S. (1998). Propagation of chaos and fluctuations for a moderate model with smooth initial data. Ann. Inst. Henri Poincaré Probab. Stat. 34 727-766.
-
(1998)
Ann. Inst. Henri Poincaré Probab. Stat.
, vol.34
, pp. 727-766
-
-
Jourdain, B.1
Andméléard, S.2
-
23
-
-
0003282323
-
Introduction to the theory of diffusion processes. Translations of Mathematical Monographs
-
Providence, RI.
-
KRYLOV, N. V. (1995). Introduction to the Theory of Diffusion Processes. Translations of Mathematical Monographs. Amer. Math. Soc., Providence, RI.
-
(1995)
Amer. Math. Soc.
-
-
Krylov, N.V.1
-
24
-
-
79955615554
-
Quenched limits and fluctuations of the empirical measure for plane rotators in random media
-
LUÇON, E. (2011). Quenched limits and fluctuations of the empirical measure for plane rotators in random media. Electron. J. Probab. 16 792-829.
-
(2011)
Electron. J. Probab.
, vol.16
, pp. 792-829
-
-
Luçon, E.1
-
25
-
-
21144445368
-
Convergence to equilibrium for granular media equations and their Euler schemes
-
MALRIEU, F. (2003). Convergence to equilibrium for granular media equations and their Euler schemes. Ann. Appl. Probab. 13 540-560.
-
(2003)
Ann. Appl. Probab.
, vol.13
, pp. 540-560
-
-
Malrieu, F.1
-
26
-
-
41349085147
-
Synchronization of oscillators with long range interaction: Phase transition and anomalous finite size effects
-
MARÓDI, M., DOVIDIO, F. and VICSEK, T. (2002). Synchronization of oscillators with long range interaction: Phase transition and anomalous finite size effects. Phys. Rev. E, 66 011109.
-
(2002)
Phys. Rev. E
, vol.66
, pp. 011109
-
-
Maródi, M.1
Dovidio, F.2
Vicsek, T.3
-
27
-
-
0003002903
-
Propagation of chaos for a class of non-linear parabolic equations
-
(Lecture Series in Differential Equations, Session 7, Catholic Univ., 1967), Air Force Office Sci. Res., Arlington, VA
-
MCKEAN, H. P. Jr. (1967). Propagation of chaos for a class of non-linear parabolic equations. In Stochastic Differential Equations (Lecture Series in Differential Equations, Session 7, Catholic Univ., 1967) 41-57. Air Force Office Sci. Res., Arlington, VA.
-
(1967)
Stochastic Differential Equations
, pp. 41-57
-
-
Mckean, Jr.H.P.1
-
28
-
-
0000669223
-
A propagation of chaos result for a system of particles with moderate interaction
-
MÉLÉARD, S. and ROELLY-COPPOLETTA, S. (1987). A propagation of chaos result for a system of particles with moderate interaction. Stochastic Process. Appl. 26 317-332.
-
(1987)
Stochastic Process. Appl.
, vol.26
, pp. 317-332
-
-
Méléard, S.1
Roelly-Coppoletta, S.2
-
29
-
-
0040554658
-
A martingale approach to the law of large numbers for weakly interacting stochastic processes
-
OELSCHLÄGER, K. (1984). A martingale approach to the law of large numbers for weakly interacting stochastic processes. Ann. Probab. 12 458-479.
-
(1984)
Ann. Probab.
, vol.12
, pp. 458-479
-
-
Oelschläger, K.1
-
30
-
-
51249177449
-
A law of large numbers for moderately interacting diffusion processes
-
OELSCHLÄGER, K. (1985). A law of large numbers for moderately interacting diffusion processes. Z. Wahrsch. Verw. Gebiete 69 279-322
-
(1985)
Z. Wahrsch Verw. Gebiete
, vol.69
, pp. 279-322
-
-
Oelschläger, K.1
-
31
-
-
79960634409
-
Loss of coherence in dynamical networks: Spatial chaos and chimera states
-
OMELCHENKO, I.,MAISTRENKO, Y., HÖVEL, P. and SCHÖLL, E. (2011). Loss of coherence in dynamical networks: Spatial chaos and chimera states. Phys. Rev. Lett. 106 234102.
-
(2011)
Phys. Rev. Lett.
, vol.106
, pp. 234102
-
-
Omelchenko, I.1
Maistrenko, Y.2
Hövel, P.3
Schöll, E.4
-
32
-
-
84857766265
-
Transition from spatial coherence to incoherence in coupled chaotic systems
-
OMELCHENKO, I., RIEMENSCHNEIDER, B., HÖVEL, P.,MAISTRENKO, Y. and SCHÖLL, E. (2012). Transition from spatial coherence to incoherence in coupled chaotic systems. Phys. Rev. E, 85 026212.
-
(2012)
Phys. Rev. E
, vol.85
, pp. 026212
-
-
Omelchenko, I.1
Riemenschneider, B.2
Hövel, P.3
Maistrenko, Y.4
Schöll, E.5
-
33
-
-
0001042755
-
Phase transitions in nonlinear oscillator chains
-
ROGERS, J. L. andWILLE, L. T. (1996). Phase transitions in nonlinear oscillator chains. Phys. Rev. E, 54 R2193-R2196.
-
(1996)
Phys. Rev. E
, vol.54
-
-
Rogers, J.L.1
Wille, L.T.2
-
34
-
-
1542499302
-
Stability of incoherence in a population of coupled oscillators
-
STROGATZ, S. H. and MIROLLO, R. E. (1991). Stability of incoherence in a population of coupled oscillators. J. Stat. Phys. 63 613-635.
-
(1991)
J. Stat. Phys.
, vol.63
, pp. 613-635
-
-
Strogatz, S.H.1
Mirollo, R.E.2
-
35
-
-
0001293553
-
Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated
-
SZNITMAN, A.-S. (1984). Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated. J. Funct. Anal. 56 311-336
-
(1984)
J. Funct. Anal.
, vol.56
, pp. 311-336
-
-
Sznitman, A.-S.1
-
36
-
-
0001105004
-
Topics in propagation of chaos
-
In École D'Été de Probabilités de Saint-Flour XIX- 1989, Springer, Berlin
-
SZNITMAN, A.-S. (1991). Topics in propagation of chaos. In École D'Été de Probabilités de Saint-Flour XIX - 1989. Lecture Notes in Math. 1464 165-251. Springer, Berlin.
-
(1991)
Lecture Notes in Math.
, vol.1464
, pp. 165-251
-
-
Sznitman, A.-S.1
-
38
-
-
84870340226
-
Limits and dynamics of stochastic neuronal networks with random heterogeneous delays
-
TOUBOUL, J. (2012). Limits and dynamics of stochastic neuronal networks with random heterogeneous delays. J. Stat. Phys. 149 569-597.
-
(2012)
J. Stat. Phys.
, vol.149
, pp. 569-597
-
-
Touboul, J.1
-
40
-
-
84875033427
-
Topological and dynamical complexity of random neural networks
-
WAINRIB, G. and TOUBOUL, J. (2013). Topological and dynamical complexity of random neural networks. Phys. Rev. Lett. 110 118101.
-
(2013)
Phys. Rev. Lett.
, vol.110
, pp. 118101
-
-
Wainrib, G.1
Touboul, J.2
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