The Kuramoto model: A simple paradigm for synchronization phenomena, Reviews of Modern Physics, vol.77, issue.1, pp.137-185, 2005. ,
DOI : 10.1103/RevModPhys.77.137
Liapunov functionals and large-time-asymptotics of mean-field nonlinear Fokker-Planck equations, Transport Theory and Statistical Physics, vol.16, issue.7, pp.733-751, 1996. ,
DOI : 10.1080/00411459608203544
Non-negative solutions of linear parabolic equations, Ann. Scuola Norm. Sup. Pisa, vol.22, pp.607-694, 1968. ,
Exit asymptotics for small diffusion about an unstable equilibrium. Stochastic Process, Appl, vol.118, pp.839-851, 2008. ,
Invariant manifolds and foliations for semiflow, p.129, 1998. ,
The Eyring-Kramers law for potentials with nonquadratic saddles, Markov Processes Relat. Fields, vol.16, pp.549-598, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00294931
Soft and Hard Wall in a Stochastic Reaction Diffusion Equation, Archive for Rational Mechanics and Analysis, vol.1, issue.2, pp.307-345, 2008. ,
DOI : 10.1007/s00205-008-0154-0
Front Fluctuations in One Dimensional Stochastic Phase Field Equations, Annales Henri Poincar??, vol.3, issue.1, pp.29-86, 2002. ,
DOI : 10.1007/s00023-002-8611-z
Dynamical Aspects of Mean Field Plane Rotators and??the??Kuramoto Model, Journal of Statistical Physics, vol.63, issue.3, pp.270-290, 2010. ,
DOI : 10.1007/s10955-009-9908-9
URL : https://hal.archives-ouvertes.fr/hal-00497541
Synchronisation and random long time dynamics for mean-field plane rotators, 2013. ,
Stable nonequilibrium probability densities and phase transitions for meanfield models in the thermodynamic limit, Journal of Statistical Physics, vol.128, issue.3-4, pp.659-678, 1987. ,
DOI : 10.1007/BF01013379
Metastability in Reversible Diffusion Processes I: Sharp Asymptotics for Capacities and Exit Times, Journal of the European Mathematical Society, vol.6, pp.399-424, 2004. ,
DOI : 10.4171/JEMS/14
Interface Fluctuations for the D = 1 Stochastic Ginzburg???Landau Equation with Nonsymmetric Reaction Term, Journal of Statistical Physics, vol.93, issue.5/6, pp.1111-1142, 1998. ,
DOI : 10.1023/B:JOSS.0000033154.54515.e8
Interface fluctuations and couplings in the d=1 Ginzburg-Landau equation with noise, Journal of Theoretical Probability, vol.11, issue.1, pp.25-80, 1998. ,
DOI : 10.1023/A:1021642824394
Brownian fluctuations of the interface in the d = 1 Ginzburg-Landau equation with noise, Annal. Inst. H. Poincaré, vol.31, pp.81-118, 1995. ,
Functional analysis, Sobolev spaces and partial differential equations, 2011. ,
DOI : 10.1007/978-0-387-70914-7
Synchronous Rhythmic Flashing of Fireflies. II., The Quarterly Review of Biology, vol.63, issue.3, pp.265-289, 1988. ,
DOI : 10.1086/415929
KINETIC LIMITS FOR PAIR-INTERACTION DRIVEN MASTER EQUATIONS AND BIOLOGICAL SWARM MODELS, Mathematical Models and Methods in Applied Sciences, vol.23, issue.07, 2012. ,
DOI : 10.1142/S0218202513500115
URL : https://hal.archives-ouvertes.fr/hal-00625542
The role of disorder in the dynamics of critical fluctuations of mean field models, Electronic Journal of Probability, vol.17, issue.0, pp.1-40, 2012. ,
DOI : 10.1214/EJP.v17-1896
Asymptotic states of a Smoluchowski equation. Archive for Rational Mechanics and Analysis, pp.365-384, 2004. ,
McKean-Vlasov limit for interacting random processes in random media, Journal of Statistical Physics, vol.56, issue.3-4, pp.735-772, 1996. ,
DOI : 10.1007/BF02179656
A Curie-Weiss Model with Dissipation, Journal of Statistical Physics, vol.19, issue.11, pp.37-53, 2013. ,
DOI : 10.1007/s10955-013-0756-2
On the exponential exit law in the small parameter exit problem, Stochastics, vol.17, issue.4, pp.297-323, 1983. ,
DOI : 10.1080/17442508308833244
Large deviations results for the exit problem with characteristic boundary, Journal of Mathematical Analysis and Applications, vol.147, issue.1, pp.134-153, 1990. ,
DOI : 10.1016/0022-247X(90)90389-W
Some regularity results on the Ventcel-Freidlin quasi-potential function, Applied Mathematics & Optimization, vol.25, issue.1, pp.259-282, 1985. ,
DOI : 10.1007/BF01442211
Microscopic versus macroscopic approaches to non-equilibrium systems, Journal of Statistical Mechanics: Theory and Experiment, vol.2011, issue.01, p.1030, 2011. ,
DOI : 10.1088/1742-5468/2011/01/P01030
URL : http://arxiv.org/abs/1012.1136
The theory of polymer dynamics. Oxford science publications, 1988. ,
Linear operators. Part II, 1988. ,
Parabolic Bursting in an Excitable System Coupled with a Slow Oscillation, SIAM Journal on Applied Mathematics, vol.46, issue.2, pp.233-253, 1986. ,
DOI : 10.1137/0146017
Multiple pulse interactions and averaging in systems of coupled neural oscillators, Journal of Mathematical Biology, vol.23, issue.3, pp.195-217, 1991. ,
DOI : 10.1007/BF00160535
The Activated Complex in Chemical Reactions, The Journal of Chemical Physics, vol.3, issue.2, pp.107-115, 1935. ,
DOI : 10.1063/1.1749604
A Hilbertian approach for fluctuations on the McKean-Vlasov model. Stochastic Process, Appl, vol.71, pp.33-53, 1997. ,
Random Perturbations of dynamical systems. Grundlehren der Mathematischen Wissenschaften Series, 1998. ,
Partial Differential Equations of Parabolic Type, N. J, 1964. ,
The scaling limit for a stochastic PDE and the separation of phases, Probability Theory and Related Fields, vol.71, issue.2, pp.221-288, 1995. ,
DOI : 10.1007/BF01213390
Zero temperature limit for interacting Brownian particles. I. Motion of a single body, The Annals of Probability, vol.32, issue.2, pp.1201-12271228, 2004. ,
DOI : 10.1214/009117904000000180
Metastability for a class dynamical systems subject to small random perturbations. The Annals of Probability, pp.1288-1305, 1987. ,
On the McKean-Vlasov Limit for Interacting Diffusions, Mathematische Nachrichten, vol.44, issue.1, pp.197-248, 1988. ,
DOI : 10.1002/mana.19881370116
Deterministic and stochastic hydrodynamic equations arising from simple microscopic model systems, Stochastic partial differential equations: six perspectives, pp.107-152, 1999. ,
DOI : 10.1090/surv/064/03
Coherence Stability and Effect of Random Natural Frequencies in Populations of Coupled Oscillators, Journal of Dynamics and Differential Equations, vol.63, issue.2 ,
DOI : 10.1007/s10884-014-9370-5
URL : https://hal.archives-ouvertes.fr/hal-01018542
Global attractor and asymptotic dynamics in the Kuramoto model for coupled noisy phase oscillators, Nonlinearity, vol.25, issue.5, pp.1247-1273, 2012. ,
DOI : 10.1088/0951-7715/25/5/1247
URL : https://hal.archives-ouvertes.fr/hal-00705301
Transitions in Active Rotator Systems: Invariant Hyperbolic Manifold Approach, SIAM Journal on Mathematical Analysis, vol.44, issue.6, pp.4165-4194, 2012. ,
DOI : 10.1137/110846452
URL : https://hal.archives-ouvertes.fr/hal-00783567
Dynamics of Limit-Cycle Oscillators Subject to General Noise, Physical Review Letters, vol.105, issue.15, p.154101, 2010. ,
DOI : 10.1103/PhysRevLett.105.154101
Normally hyperbolic invariant manifolds in dynamical systems, 1994. ,
Interacting Coherence Resonance Oscillators, Physical Review Letters, vol.83, issue.9, pp.1771-1774, 1999. ,
DOI : 10.1103/PhysRevLett.83.1771
Dynamical mean-field approximation to coupled active rotator networks subject to white noises. arXiv:cond-mat, 210473. ,
Periodic long time behaviour for an approximate model of nematic polymers. Kinetic and related models, pp.357-382, 2012. ,
URL : https://hal.archives-ouvertes.fr/inria-00609763
Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, vol.840, 1981. ,
DOI : 10.1007/BFb0089647
Invariant manifolds, Lecture Notes in Mathematics, vol.583, 1977. ,
Tightness problem and stochastic evolution equation arising from fluctuation phenomena for interacting diffusions, Journal of Multivariate Analysis, vol.19, issue.2, pp.311-328, 1986. ,
DOI : 10.1016/0047-259X(86)90035-7
Theory of dynamic critical phenomena, Reviews of Modern Physics, vol.49, issue.3, pp.435-479, 1977. ,
DOI : 10.1103/RevModPhys.49.435
Large deviations, Fields Institute Monographs. AMS, vol.14, 2000. ,
DOI : 10.1090/fim/014
Dynamical systems in neuroscience: The geometry of excitability and bursting, 2007. ,
Limit theorems for stochastic processes, of Grundlehren der Mathematischen Wissenschaften, 2003. ,
DOI : 10.1007/978-3-662-02514-7
Perturbation theory for linear operators, Classics in Mathematics, 1995. ,
Scaling Limits of Interacting Particle Systems, volume 320 of Grundlehren der mathematischen Wissenschaften, 1999. ,
Respiratory-Like Rhythmic Activity Can Be Produced by an Excitatory Network of Non-Pacemaker Neuron Models, Journal of Neurophysiology, vol.92, issue.2, pp.686-699, 2004. ,
DOI : 10.1152/jn.00046.2004
Theory of phase locking of globally coupled laser arrays, Physical Review A, vol.52, issue.5, pp.4089-4094, 1995. ,
DOI : 10.1103/PhysRevA.52.4089
Brownian motion in a field of force and the diffusion model of chemical reactions, Physica, vol.7, issue.4, pp.284-304, 1940. ,
DOI : 10.1016/S0031-8914(40)90098-2
Chemical oscillations, waves, and turbulence. Dover Books on Chemistry Series, 2003. ,
DOI : 10.1007/978-3-642-69689-3
Noise-induced synchronous neuronal oscillations, Physical Review E, vol.51, issue.6, pp.6213-6218, 1995. ,
DOI : 10.1103/PhysRevE.51.6213
Effects of noise in excitable systems, Physics Reports, vol.392, issue.6, pp.321-424, 2004. ,
DOI : 10.1016/j.physrep.2003.10.015
Large time asymptotics for the fluctuation SPDE in the Kuramoto synchronization model, pp.1204-2176 ,
Quenched Limits and Fluctuations of the Empirical Measure for Plane Rotators in Random Media., Electronic Journal of Probability, vol.16, issue.0, pp.792-829, 2011. ,
DOI : 10.1214/EJP.v16-874
Computer simulation of rhythmic oscillations in neuron pools, Kybernetik, vol.2, issue.2, pp.79-86, 1974. ,
DOI : 10.1007/BF00271630
A scaling theory of bifurcations in the symmetric weak-noise escape problem, Journal of Statistical Physics, vol.68, issue.FS 14, pp.291-357, 1996. ,
DOI : 10.1007/BF02183736
A description of the liquid-crystalline phase of rodlike polymers at high shear rates, Macromolecules, vol.22, issue.10, pp.4076-4082, 1989. ,
DOI : 10.1021/ma00200a045
Small random perturbations of finite- and infinite-dimensional dynamical systems: Unpredictability of exit times, Journal of Statistical Physics, vol.4, issue.4, pp.477-504, 1989. ,
DOI : 10.1007/BF01041595
Propagation of chaos for a class of non-parabolic equations. Stochastic differential equations, pp.41-57, 1967. ,
Linear differential operators. Part I: Elementary theory of linear differential operators, 1967. ,
A Martingale Approach to the Law of Large Numbers for Weakly Interacting Stochastic Processes, The Annals of Probability, vol.12, issue.2, pp.458-479, 1984. ,
DOI : 10.1214/aop/1176993301
Critical phenomena in globally coupled excitable elements, Physical Review E, vol.78, issue.6, p.65101, 2008. ,
DOI : 10.1103/PhysRevE.78.065101
Large Deviations and Metastability, volume 100 of Encyclopedia of Mathematics and its Applications, 2005. ,
Regular travelling waves in a onedimensional network of theta neurons Eulerian calculus for the contraction in the wasserstein distance, SIAM J. Appl. Math. SIAM J. Math. Anal, vol.37, pp.1197-12211227, 2002. ,
Dynamics of a structured neuron population, Nonlinearity, vol.23, issue.1, pp.55-75, 2010. ,
DOI : 10.1088/0951-7715/23/1/003
URL : https://hal.archives-ouvertes.fr/hal-00387413
Noise-induced phase transitions in globally coupled active rotators, Physical Review E, vol.53, issue.4, pp.3425-3430, 1996. ,
DOI : 10.1103/PhysRevE.53.3425
Stable Rotating Waves in Two-Dimensional Discrete Active Media, SIAM Journal on Applied Mathematics, vol.54, issue.6, pp.1720-1744, 1994. ,
DOI : 10.1137/S0036139993250683
Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol.44, 1983. ,
DOI : 10.1007/978-1-4612-5561-1
Mean-field bounds on the magnetization for ferromagnetic spin models, Journal of Statistical Physics, vol.27, issue.2, pp.309-290, 1981. ,
DOI : 10.1007/BF01022189
Mathematical aspect of heart physiology, Courant Institute of Mathematical Science Publication, 1975. ,
Activity in sparsely connected excitatory neural networks: effect of connectivity, Neural Networks, vol.11, issue.3, pp.415-434, 1998. ,
DOI : 10.1016/S0893-6080(97)00153-6
Noise-induced coherent oscillations in randomly connected neural networks, Physical Review E, vol.58, issue.3, pp.3610-3622, 1998. ,
DOI : 10.1103/PhysRevE.58.3610
Finite-size effects in a population of interacting oscillators, Physical Review E, vol.59, issue.2, pp.1633-1636, 1998. ,
DOI : 10.1103/PhysRevE.59.1633
Synchronization: A Universal Concept in Nonlinear Sciences, 2003. ,
DOI : 10.1017/CBO9780511755743
Coherence Resonance in a Noise-Driven Excitable System, Physical Review Letters, vol.78, issue.5, pp.775-778, 1997. ,
DOI : 10.1103/PhysRevLett.78.775
Phase reduction in the noise induced escape problem for systems close to reversibility, Stochastic Processes and their Applications, vol.124, issue.10 ,
DOI : 10.1016/j.spa.2014.05.003
URL : https://hal.archives-ouvertes.fr/hal-01061157
Scaling limits in statistical mechanics and microstructures in continuum mechanics. Theoretical and Mathematical Physics, 2009. ,
Noise-Induced Coherence in Neural Networks, Physical Review Letters, vol.77, issue.15, pp.3256-3259, 1996. ,
DOI : 10.1103/PhysRevLett.77.3256
Methods of modern mathematical physics. I. Functional analysis, 1980. ,
Spontaneous Resonances and the Coherent States of??the??Queuing Networks, Journal of Statistical Physics, vol.1, issue.4, pp.67-104, 2009. ,
DOI : 10.1007/s10955-008-9658-0
URL : https://hal.archives-ouvertes.fr/hal-00176074
Cooperative Phenomena in Coupled Oscillator Systems under External Fields, Progress of Theoretical Physics, vol.79, issue.1, pp.39-46, 1988. ,
DOI : 10.1143/PTP.79.39
Phase Transitions and Their Bifurcation Analysis in a Large Population of Active Rotators with Mean-Field Coupling, Progress of Theoretical Physics, vol.79, issue.3, pp.600-607, 1988. ,
DOI : 10.1143/PTP.79.600
Noise can create periodic behavior and stabilize nonlinear diffusions, Stochastic Processes and their Applications, vol.20, issue.2, pp.323-331, 1985. ,
DOI : 10.1016/0304-4149(85)90219-4
URL : http://doi.org/10.1016/0304-4149(85)90219-4
Some Examples of Nonlinear Diffusion Processes Having a Time-Periodic Law, The Annals of Probability, vol.13, issue.2, pp.379-384, 1985. ,
DOI : 10.1214/aop/1176992997
Periodic behavior of the stochastic Brusselator in the mean-field limit, Probability Theory and Related Fields, vol.11, issue.3, pp.425-462, 1986. ,
DOI : 10.1007/BF00334195
Dynamics of evolutionary equations, Applied Mathematical Sciences, vol.143, 2002. ,
DOI : 10.1007/978-1-4757-5037-9
Cooperative Phenomena in Two-Dimensional Active Rotator Systems, Progress of Theoretical Physics, vol.75, issue.6, pp.1319-1327, 1986. ,
DOI : 10.1143/PTP.75.1319
Phase Transitions in Active Rotator Systems, Progress of Theoretical Physics, vol.75, issue.5, pp.1105-1110, 1986. ,
DOI : 10.1143/PTP.75.1105
A Class of Mean Field Models, Journal of Mathematical Physics, vol.13, issue.4, pp.468-474, 1972. ,
DOI : 10.1063/1.1666002
Stability of incoherence in a population of coupled oscillators, Journal of Statistical Physics, vol.60, issue.3-4, pp.613-635, 1991. ,
DOI : 10.1007/BF01029202
From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators, Physica D: Nonlinear Phenomena, vol.143, issue.1-4, pp.1-20, 2000. ,
DOI : 10.1016/S0167-2789(00)00094-4
Sync: The Emerging Science of Spontaneous Order, 2003. ,
Multidimensional diffusion processes, Classics in Mathematics, 2006. ,
DOI : 10.1007/3-540-28999-2
Topics in propagation of chaos InÉcoleIn´InÉcole d'´ eté de probabilités de Saint-Flour XIX?1989, Lecture Notes in Math, vol.1464, 1991. ,
Stochastic Phase Reduction for a General Class of Noisy Limit Cycle Oscillators, Physical Review Letters, vol.102, issue.19, 2009. ,
DOI : 10.1103/PhysRevLett.102.194102
System size coherence resonance in coupled FitzHugh-Nagumo models, Europhysics Letters (EPL), vol.61, issue.2, pp.162-167, 2003. ,
DOI : 10.1209/epl/i2003-00207-5
Noise-Induced Behaviors in Neural Mean Field Dynamics, SIAM Journal on Applied Dynamical Systems, vol.11, issue.1, pp.49-81, 2012. ,
DOI : 10.1137/110832392
URL : https://hal.archives-ouvertes.fr/hal-00846146
Coherence resonance and noise-induced synchronization in globally coupled Hodgkin-Huxley neurons, Physical Review E, vol.61, issue.1, pp.740-746, 2000. ,
DOI : 10.1103/PhysRevE.61.740
Coherence resonance and noise-induced synchronization in Hindmarsh-Rose neural network with different topologies, Commun. Theor. Phys, vol.48, p.759, 2007. ,
Phase Reduction of Stochastic Limit Cycle Oscillators, Physical Review Letters, vol.101, issue.15, p.154101, 2008. ,
DOI : 10.1103/PhysRevLett.101.154101