메뉴 건너뛰기




Volumn 29, Issue 2, 2015, Pages 460-493

Noise, interaction, nonlinear dynamics and the origin of rhythmic behaviors

Author keywords

Coupled excitable systems; Coupled stochastic rotators; Fokker Planck PDE; Kuramoto synchronization model; Normally contracting manifold; Rhythmic behaviors

Indexed keywords


EID: 84927922578     PISSN: 01030752     EISSN: None     Source Type: Journal    
DOI: 10.1214/14-BJPS258     Document Type: Article
Times cited : (35)

References (52)
  • 2
    • 0030376634 scopus 로고    scopus 로고
    • Liapunov functionals and large-timeasymptotics of mean-field nonlinear Fokker–Planck equations
    • MR1420187
    • Arnold, A., Bonilla, L. L. and Markowich, P. A. (1996). Liapunov functionals and large-timeasymptotics of mean-field nonlinear Fokker–Planck equations. Transport Theory Statist. Phys. 25, 733–751. MR1420187
    • (1996) Transport Theory Statist. Phys , vol.25 , pp. 733-751
    • Arnold, A.1    Bonilla, L.L.2    Markowich, P.A.3
  • 3
    • 0000377165 scopus 로고
    • Non-negative solutions of linear parabolic equations
    • MR0435594
    • Aronson, D. G. (1968). Non-negative solutions of linear parabolic equations. Ann. Scuola Norm. Sup. Pisa (3) 22, 607–694. MR0435594
    • (1968) Ann. Scuola Norm. Sup. Pisa (3) , vol.22 , pp. 607-694
    • Aronson, D.G.1
  • 5
    • 33748109655 scopus 로고    scopus 로고
    • Existence and persistence of invariant manifolds for semiflows in Banach space
    • MR1445489
    • Bates, P. W., Lu, K. and Zeng, C. (1998). Existence and persistence of invariant manifolds for semiflows in Banach space. Mem. Amer. Math. Soc. 135, 1–129. MR1445489
    • (1998) Mem. Amer. Math. Soc , vol.135 , pp. 1-129
    • Bates, P.W.1    Lu, K.2    Zeng, C.3
  • 7
    • 77249132487 scopus 로고    scopus 로고
    • Dynamical aspects of mean field plane rotators and the Kuramoto model
    • MR2594897
    • Bertini, L., Giacomin, G. and Pakdaman, K. (2010). Dynamical aspects of mean field plane rotators and the Kuramoto model. J. Stat. Phys. 138, 270–290. MR2594897
    • (2010) J. Stat. Phys , vol.138 , pp. 270-290
    • Bertini, L.1    Giacomin, G.2    Pakdaman, K.3
  • 8
    • 84911990278 scopus 로고    scopus 로고
    • Synchronization and random long time dynamics for mean-field plane rotators
    • MR3278917
    • Bertini, L., Giacomin, G. and Poquet, C. (2014). Synchronization and random long time dynamics for mean-field plane rotators. Probab. Theory Related Fields 160, 593–653. MR3278917
    • (2014) Probab. Theory Related Fields , vol.160 , pp. 593-653
    • Bertini, L.1    Giacomin, G.2    Poquet, C.3
  • 9
    • 0000122907 scopus 로고
    • Order function and macroscopic mutual entrainment in uniformly coupled limitcycle oscillators
    • Daido, H. (1992). Order function and macroscopic mutual entrainment in uniformly coupled limitcycle oscillators. Progr. Theoret. Phys. Suppl. 88, 1213–1218.
    • (1992) Progr. Theoret. Phys. Suppl , vol.88 , pp. 1213-1218
    • Daido, H.1
  • 10
    • 84878801028 scopus 로고    scopus 로고
    • A Curie–Weiss model with dissipation
    • MR3067075
    • Dai Pra, P., Fischer, M. and Regoli, D. (2013). A Curie–Weiss model with dissipation. J. Stat. Phys. 152, 37–53. MR3067075
    • (2013) J. Stat. Phys , vol.152 , pp. 37-53
    • Dai Pra, P.1    Fischer, M.2    Regoli, D.3
  • 11
    • 0030210666 scopus 로고    scopus 로고
    • McKean–Vlasov limit for interacting random processes in random media
    • MR1400186
    • Dai Pra, P. and den Hollander, F. (1996). McKean–Vlasov limit for interacting random processes in random media. J. Stat. Phys. 84, 735–772. MR1400186
    • (1996) J. Stat. Phys , vol.84 , pp. 735-772
    • Dai Pra, P.1    Den Hollander, F.2
  • 12
    • 79751499053 scopus 로고    scopus 로고
    • Microscopic versus macroscopic approaches to non-equilibrium systems
    • MR2770606
    • Derrida, B. (2011). Microscopic versus macroscopic approaches to non-equilibrium systems. J. Stat. Mech. Theory Exp. 2011, P01030. MR2770606
    • (2011) J. Stat. Mech. Theory Exp , vol.2011
    • Derrida, B.1
  • 13
    • 0001098077 scopus 로고
    • Molecular dynamics and rheological properties of concentrated solutions of rodlike polymers in isotropic and liquid crystalline phases
    • Doi, M. (1981). Molecular dynamics and rheological properties of concentrated solutions of rodlike polymers in isotropic and liquid crystalline phases. J. Polymer Science 19, 229–243.
    • (1981) J. Polymer Science , vol.19 , pp. 229-243
    • Doi, M.1
  • 14
    • 0022693272 scopus 로고
    • Parabolic bursting in an excitable system coupled with a slow oscillation
    • MR0833476
    • Ermentrout, G. B. and Kopell, N. (1986). Parabolic bursting in an excitable system coupled with a slow oscillation. SIAM J. Appl. Math. 46, 233–253. MR0833476
    • (1986) SIAM J. Appl. Math , vol.46 , pp. 233-253
    • Ermentrout, G.B.1    Kopell, N.2
  • 15
    • 0001356311 scopus 로고
    • Persistence and smoothness of invariant manifolds for flows
    • MR0287106
    • Fenichel, N. (1971). Persistence and smoothness of invariant manifolds for flows. Indiana Univ. Math. J. 21, 193–226. MR0287106
    • (1971) Indiana Univ. Math. J , vol.21 , pp. 193-226
    • Fenichel, N.1
  • 16
    • 0031116136 scopus 로고    scopus 로고
    • Phase segregation dynamics in particle systems with long range interactions
    • MR1453735
    • Giacomin, G. and Lebowitz, J. L. (1997). Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits. J. Stat. Phys. 87, 37–61. MR1453735
    • (1997) I. Macroscopic Limits. J. Stat. Phys , vol.87 , pp. 37-61
    • Giacomin, G.1    Lebowitz, J.L.2
  • 17
    • 0032291814 scopus 로고    scopus 로고
    • Phase segregation dynamics in particle systems with long range interactions. II. Interface motion
    • MR1638739
    • Giacomin, G. and Lebowitz, J. L. (1998). Phase segregation dynamics in particle systems with long range interactions. II. Interface motion. SIAM J. Appl. Math. 58, 1707–1729. MR1638739
    • (1998) SIAM J. Appl. Math , vol.58 , pp. 1707-1729
    • Giacomin, G.1    Lebowitz, J.L.2
  • 18
    • 84901056075 scopus 로고    scopus 로고
    • Coherence stability and effect of random natural frequencies in populations of coupled oscillators
    • MR3207725
    • Giacomin, G., Luçon, E. and Poquet, C. (2014). Coherence stability and effect of random natural frequencies in populations of coupled oscillators. J. Dynam. Differential Equations 26, 333–367. MR3207725
    • (2014) J. Dynam. Differential Equations , vol.26 , pp. 333-367
    • Giacomin, G.1    Luçon, E.2    Poquet, C.3
  • 19
    • 84859795069 scopus 로고    scopus 로고
    • Global attractor and asymptotic dynamics in the Kuramoto model for coupled noisy phase oscillators
    • MR2914138
    • Giacomin, G., Pakdaman, K. and Pellegrin, X. (2012a). Global attractor and asymptotic dynamics in the Kuramoto model for coupled noisy phase oscillators. Nonlinearity 25, 1247–1273. MR2914138
    • (2012) Nonlinearity , vol.25 , pp. 1247-1273
    • Giacomin, G.1    Pakdaman, K.2    Pellegrin, X.3
  • 20
    • 84871595606 scopus 로고    scopus 로고
    • Transitions in active rotator systems: Invariant hyperbolic manifold approach
    • MR3023444
    • Giacomin, G., Pakdaman, K., Pellegrin, X. and Poquet, C. (2012b). Transitions in active rotator systems: Invariant hyperbolic manifold approach. SIAM J. Math. Anal. 44, 4165–4194. MR3023444
    • (2012) SIAM J. Math. Anal , vol.44 , pp. 4165-4194
    • Giacomin, G.1    Pakdaman, K.2    Pellegrin, X.3    Poquet, C.4
  • 21
    • 84899655348 scopus 로고    scopus 로고
    • Models in biology: ‘Accurate descriptions of our pathetic thinking’
    • Gunawardena, J. (2014). Models in biology: ‘Accurate descriptions of our pathetic thinking’. BMC Biol. 12, 1–11.
    • (2014) BMC Biol , vol.12 , pp. 1-11
    • Gunawardena, J.1
  • 22
    • 84864119983 scopus 로고    scopus 로고
    • Periodic long-time behaviour for an approximate model of nematic polymers
    • MR2911099
    • He, L., Le Bris, C. and Lelièvre, T. (2012). Periodic long-time behaviour for an approximate model of nematic polymers. Kinet. Relat. Models 5, 357–382. MR2911099
    • (2012) Kinet. Relat. Models , vol.5 , pp. 357-382
    • He, L.1    Le Bris, C.2    Lelièvre, T.3
  • 23
    • 0003304963 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • Berlin–New York: Springer, MR0610244
    • Henry, D. (1981). Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics 840. Berlin–New York: Springer. MR0610244
    • (1981) Lecture Notes in Mathematics , pp. 840
    • Henry, D.1
  • 24
    • 65549147428 scopus 로고
    • Fokker–Planck-equation approach to flow alignment in liquid crystals. Z
    • Hess, S. (1976). Fokker–Planck-equation approach to flow alignment in liquid crystals. Z. Naturforsch. 31a, 1034–1037.
    • (1976) Naturforsch , vol.31a , pp. 1034-1037
    • Hess, S.1
  • 29
    • 77951728647 scopus 로고    scopus 로고
    • On the Vlasov limit for systems of nonlinearly coupled oscillators without noise
    • MR2265477
    • Lancellotti, C. (2005). On the Vlasov limit for systems of nonlinearly coupled oscillators without noise. Transport Theory Statist. Phys. 34, 523–535. MR2265477
    • (2005) Transport Theory Statist. Phys , vol.34 , pp. 523-535
    • Lancellotti, C.1
  • 30
    • 0000578371 scopus 로고
    • A particle model for spinodal decomposition
    • MR1116042
    • Lebowitz, J., Orlandi, E. and Presutti, E. (1991). A particle model for spinodal decomposition. J. Stat. Phys. 63, 933–974. MR1116042
    • (1991) J. Stat. Phys , vol.63 , pp. 933-974
    • Lebowitz, J.1    Orlandi, E.2    Presutti, E.3
  • 31
    • 33644545098 scopus 로고    scopus 로고
    • Alignment and Rheo-oscillator criteria for sheared nematic polymer films in the monolayer limit
    • (electronic), MR2176296
    • Lee, J. H., Forest, M. G. and Zhou, R. (2006). Alignment and Rheo-oscillator criteria for sheared nematic polymer films in the monolayer limit. Discrete Contin. Dyn. Syst. Ser. B 6, 339–356 (electronic). MR2176296
    • (2006) Discrete Contin. Dyn. Syst. Ser. B , vol.6 , pp. 339-356
    • Lee, J.H.1    Forest, M.G.2    Zhou, R.3
  • 33
    • 79955615554 scopus 로고    scopus 로고
    • Quenched limits and fluctuations of the empirical measure for plane rotators in random media
    • MR2793244
    • Luçon, E. (2011). Quenched limits and fluctuations of the empirical measure for plane rotators in random media. Electron. J. Probab. 16, 792–829. MR2793244
    • (2011) Electron. J. Probab , vol.16 , pp. 792-829
    • Luçon, E.1
  • 34
    • 84863158657 scopus 로고    scopus 로고
    • Kinetic theory for nonequilibrium stationary states in long-range interacting systems
    • Nardini, C., Gupta, S., Ruffo, S., Dauxois, T. and Bouchet, F. (2012). Kinetic theory for nonequilibrium stationary states in long-range interacting systems. J. Stat. Mech. Theory Exp. 2012, L01002.
    • (2012) J. Stat. Mech. Theory Exp , vol.2012
    • Nardini, C.1    Gupta, S.2    Ruffo, S.3    Dauxois, T.4    Bouchet, F.5
  • 35
    • 84884136684 scopus 로고    scopus 로고
    • Relaxation and self-sustained oscillations in the time elapsed neuron network model
    • MR3071416
    • Pakdaman, K., Perthame, B. and Salort, D. (2013). Relaxation and self-sustained oscillations in the time elapsed neuron network model. SIAM J. Appl. Math. 73, 1260–1279. MR3071416
    • (2013) SIAM J. Appl. Math , vol.73 , pp. 1260-1279
    • Pakdaman, K.1    Perthame, B.2    Salort, D.3
  • 36
    • 0142013256 scopus 로고
    • Mean-field bounds on the magnetization for ferromagnetic spin models
    • MR0624749
    • Pearce, P. A. (1981). Mean-field bounds on the magnetization for ferromagnetic spin models. J. Stat. Phys. 25, 309–320. MR0624749
    • (1981) J. Stat. Phys , vol.25 , pp. 309-320
    • Pearce, P.A.1
  • 37
    • 1042298865 scopus 로고    scopus 로고
    • Synchronization
    • Cambridge Nonlinear Science Series, Cambridge: Cambridge Univ. Press, MR1869044
    • Pikovsky, A., Rosenblum, M. and Kurths, J. (2001). Synchronization. A Universal Concept in Nonlinear Sciences. Cambridge Nonlinear Science Series 12. Cambridge: Cambridge Univ. Press. MR1869044
    • (2001) A Universal Concept in Nonlinear Sciences , pp. 12
    • Pikovsky, A.1    Rosenblum, M.2    Kurths, J.3
  • 38
    • 70450154975 scopus 로고    scopus 로고
    • Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics
    • Berlin: Springer, MR2460018
    • Presutti, E. (2009). Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics. Theoretical and Mathematical Physics. Berlin: Springer. MR2460018
    • (2009) Theoretical and Mathematical Physics
    • Presutti, E.1
  • 39
    • 58549107783 scopus 로고    scopus 로고
    • Spontaneous resonances and the coherent states of the queuing networks
    • MR2489495
    • Rybko, A., Shlosman, S. and Vladimirov, A. (2009). Spontaneous resonances and the coherent states of the queuing networks. J. Stat. Phys. 134, 67–104. MR2489495
    • (2009) J. Stat. Phys , vol.134 , pp. 67-104
    • Rybko, A.1    Shlosman, S.2    Vladimirov, A.3
  • 40
    • 46549091328 scopus 로고
    • Noise can create periodic behavior and stabilize nonlinear diffusions
    • MR0808166
    • Scheutzow, M. (1985). Noise can create periodic behavior and stabilize nonlinear diffusions. Stochastic Process. Appl. 20, 323–331. MR0808166
    • (1985) Stochastic Process. Appl , vol.20 , pp. 323-331
    • Scheutzow, M.1
  • 41
    • 0038930098 scopus 로고
    • Periodic behavior of the stochastic Brusselator in the mean-field limit
    • MR0843504
    • Scheutzow, M. (1986). Periodic behavior of the stochastic Brusselator in the mean-field limit. Probab. Theory Related Fields 72, 425–462. MR0843504
    • (1986) Probab. Theory Related Fields , vol.72 , pp. 425-462
    • Scheutzow, M.1
  • 42
    • 0242689013 scopus 로고    scopus 로고
    • Dynamics of Evolutionary Equations
    • New York: Springer, MR1873467
    • Sell, G. and You, Y. (2002). Dynamics of Evolutionary Equations. Applied Mathematical Sciences 143. New York: Springer. MR1873467
    • (2002) Applied Mathematical Sciences , pp. 143
    • Sell, G.1    You, Y.2
  • 43
    • 0002192231 scopus 로고
    • Cooperative phenomena in coupled oscillator systems under external fields
    • MR0937229
    • Sakaguchi, H. (1988). Cooperative phenomena in coupled oscillator systems under external fields. Progr. Theoret. Phys. 79, 39–46. MR0937229
    • (1988) Progr. Theoret. Phys , vol.79 , pp. 39-46
    • Sakaguchi, H.1
  • 44
    • 0001527148 scopus 로고
    • Phase transitions and their bifurcation analysis in a large population of active rotators with mean-field coupling
    • MR0946410
    • Sakaguchi, H., Shinomoto, S. and Kuramoto, Y. (1988a). Phase transitions and their bifurcation analysis in a large population of active rotators with mean-field coupling. Progr. Theoret. Phys. 79, 600–607. MR0946410
    • (1988) Progr. Theoret. Phys , vol.79 , pp. 600-607
    • Sakaguchi, H.1    Shinomoto, S.2    Kuramoto, Y.3
  • 45
    • 0000575665 scopus 로고
    • Mutual entrainment in oscillator lattices with nonvariational type interaction
    • MR0946410
    • Sakaguchi, H., Shinomoto, S. and Kuramoto, Y. (1988b). Mutual entrainment in oscillator lattices with nonvariational type interaction. Progr. Theoret. Phys. 79, 1069–1079. MR0946410
    • (1988) Progr. Theoret. Phys , vol.79 , pp. 1069-1079
    • Sakaguchi, H.1    Shinomoto, S.2    Kuramoto, Y.3
  • 46
    • 0001723799 scopus 로고
    • Phase transitions in active rotator systems
    • Shinomoto, S. and Kuramoto, Y. (1986a). Phase transitions in active rotator systems. Progr. Theoret. Phys. Suppl. 75, 1105–1110.
    • (1986) Progr. Theoret. Phys. Suppl , vol.75 , pp. 1105-1110
    • Shinomoto, S.1    Kuramoto, Y.2
  • 47
    • 0038062375 scopus 로고
    • Cooperative phenomena in two-dimensional active rotator systems
    • Shinomoto, S. and Kuramoto, Y. (1986b). Cooperative phenomena in two-dimensional active rotator systems. Progr. Theoret. Phys. Suppl. 75, 1319–1327.
    • (1986) Progr. Theoret. Phys. Suppl , vol.75 , pp. 1319-1327
    • Shinomoto, S.1    Kuramoto, Y.2
  • 49
    • 0038108143 scopus 로고    scopus 로고
    • How Order Emerges from Chaos in the Universe, Nature, and Daily Life. New York: Hyperion Books, MR2394754
    • Strogatz, S. (2003). Sync. How Order Emerges from Chaos in the Universe, Nature, and Daily Life. New York: Hyperion Books. MR2394754
    • (2003) Sync
    • Strogatz, S.1
  • 50
    • 67650506868 scopus 로고    scopus 로고
    • Stochastic phase reduction for a general class of noisy limit cycle oscillators
    • Teramae, J., Nakao, H. and Ermentrout, G. B. (2009). Stochastic phase reduction for a general class of noisy limit cycle oscillators. Phys. Rev. Lett. 102, 194102.
    • (2009) Phys. Rev. Lett , vol.102 , pp. 194102
    • Teramae, J.1    Nakao, H.2    Ermentrout, G.B.3
  • 51
    • 84861617067 scopus 로고    scopus 로고
    • Noise-induced behaviors in neural mean field dynamics
    • MR2902610
    • Touboul, J., Hermann, G. and Faugeras, O. (2012). Noise-induced behaviors in neural mean field dynamics. SIAM J. Appl. Dyn. Syst. 11, 49–81. MR2902610
    • (2012) SIAM J. Appl. Dyn. Syst , vol.11 , pp. 49-81
    • Touboul, J.1    Hermann, G.2    Faugeras, O.3
  • 52
    • 54049109601 scopus 로고    scopus 로고
    • Phase reduction of stochastic limit cycle oscillators
    • Yushimura, K. and Arai, K. (2008). Phase reduction of stochastic limit cycle oscillators. Phys. Rev. Lett. 101, 154101.
    • (2008) Phys. Rev. Lett , vol.101 , pp. 154101
    • Yushimura, K.1    Arai, K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.