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Volumn 240, Issue 8, 2011, Pages 719-731

Analytic approximations of statistical quantities and response of noisy oscillators

Author keywords

Asymptotic formulas; Frequency response; Multiplicative noise; Phase oscillators; Time varying FokkerPlanck; Weak noise

Indexed keywords

DYNAMIC RESPONSE; FREQUENCY RESPONSE; OSCILLATORS (MECHANICAL); PHASE NOISE;

EID: 79951511764     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2010.12.004     Document Type: Article
Times cited : (12)

References (62)
  • 3
    • 19944385353 scopus 로고    scopus 로고
    • The Kuramoto model: A simple paradigm for synchronization phenomena
    • DOI 10.1103/RevModPhys.77.137
    • J.A. Acebrn, L.L. Bonilla, C.J. Prez Vicente, F. Ritort, and R. Spigler The Kuramoto model: a simple paradigm for synchronization phenomena Rev. Modern Phys. 77 2005 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
  • 5
    • 0032678448 scopus 로고    scopus 로고
    • Weakly pulse-coupled oscillators, FM interactions, synchronization, and oscillatory associative memory
    • E.M. Izhikevich Weakly pulse-coupled oscillators, FM interactions, synchronization, and oscillatory associative memory IEEE Trans. Neural Net. 10 1999 508 526
    • (1999) IEEE Trans. Neural Net. , vol.10 , pp. 508-526
    • Izhikevich, E.M.1
  • 8
    • 29444442092 scopus 로고
    • Intrinsic fluctuations and a phase transition in a class of large populations of interacting oscillators
    • H. Daido Intrinsic fluctuations and a phase transition in a class of large populations of interacting oscillators J. Stat. Phys. 60 1990 753 800
    • (1990) J. Stat. Phys. , vol.60 , pp. 753-800
    • Daido, H.1
  • 9
    • 1542499302 scopus 로고
    • Stability of incoherence in a population of coupled oscillators
    • S.H. Strogatz, and R.E. Mirollo Stability of incoherence in a population of coupled oscillators J. Stat. Phys. 63 1991 613 635
    • (1991) J. Stat. Phys. , vol.63 , pp. 613-635
    • Strogatz, S.H.1    Mirollo, R.E.2
  • 11
    • 0025567093 scopus 로고
    • Synchronization of pulse-coupled biological oscillators
    • R.E. Mirollo, and S. Strogatz Synchronization of pulse-coupled biological oscillators SIAM J. App. Math. 50 1990 1645 1662
    • (1990) SIAM J. App. Math. , vol.50 , pp. 1645-1662
    • Mirollo, R.E.1    Strogatz, S.2
  • 13
    • 13844299470 scopus 로고    scopus 로고
    • The combined effects of inhibitory and electrical synapses in synchrony
    • DOI 10.1162/0899766053019917
    • B. Pfeuty, G. Mato, D. Golomb, and D. Hansel The combined effects of inhibitory and electrical synapses in synchrony Neural Comput. 17 2005 633 670 (Pubitemid 40251351)
    • (2005) Neural Computation , vol.17 , Issue.3 , pp. 633-670
    • Pfeuty, B.1    Mato, G.2    Golomb, D.3    Hansel, D.4
  • 14
    • 33645578085 scopus 로고    scopus 로고
    • Correlation-induced synchronization of oscillations in olfactory bulb neurons
    • R. Galn, N. Fourcaud, G.B. Ermentrout, and N.N. Urban Correlation-induced synchronization of oscillations in olfactory bulb neurons J. Neurosci. 26 2006 3646 3655
    • (2006) J. Neurosci. , vol.26 , pp. 3646-3655
    • Galn, R.1    Fourcaud, N.2    Ermentrout, G.B.3    Urban, N.N.4
  • 15
    • 1542499302 scopus 로고
    • Stability of incoherence in a population of coupled oscillators
    • S.H. Strogatz, and R.E. Mirollo Stability of incoherence in a population of coupled oscillators J. Stat. Phys. 63 1991 613 635
    • (1991) J. Stat. Phys. , vol.63 , pp. 613-635
    • Strogatz, S.H.1    Mirollo, R.E.2
  • 16
    • 0001063041 scopus 로고
    • Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators
    • L.L. Bonilla, J.C. Neu, and R. Spigler Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators J. Stat. Phys. 67 1992 313 330
    • (1992) J. Stat. Phys. , vol.67 , pp. 313-330
    • Bonilla, L.L.1    Neu, J.C.2    Spigler, R.3
  • 17
    • 21344481602 scopus 로고
    • Amplitude expansions for instabilities in populations of globally-coupled oscillators
    • J. Crawford Amplitude expansions for instabilities in populations of globally-coupled oscillators J. Stat. Phys. 74 1994 1047 1084
    • (1994) J. Stat. Phys. , vol.74 , pp. 1047-1084
    • Crawford, J.1
  • 18
    • 22244479715 scopus 로고    scopus 로고
    • Time-periodic phases in populations of nonlinearly coupled oscillators with bimodal frequency distributions
    • PII S0167278997001875
    • L.L. Bonilla, C.J. Prez Vicente, and R. Spigler Time-periodic phases in populations of nonlinearly coupled oscillators with bimodal frequency distributions Physica D 113 1998 79 97 (Pubitemid 128676487)
    • (1998) Physica D: Nonlinear Phenomena , vol.113 , Issue.1 , pp. 79-97
    • Bonilla, L.L.1    Perez Vicente, C.J.2    Spigler, R.3
  • 19
    • 19744369589 scopus 로고    scopus 로고
    • Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators
    • J. Teramae, and D. Tanaka Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators Phys. Rev. Lett. 93 2004 204103
    • (2004) Phys. Rev. Lett. , vol.93 , pp. 204103
    • Teramae, J.1    Tanaka, D.2
  • 20
  • 21
    • 34548836370 scopus 로고    scopus 로고
    • Correlations, fluctuations, and stability of a finite-size network of coupled oscillators
    • M. Buice, and C. Chow Correlations, fluctuations, and stability of a finite-size network of coupled oscillators Phys. Rev. E 76 2007 031118
    • (2007) Phys. Rev. e , vol.76 , pp. 031118
    • Buice, M.1    Chow, C.2
  • 22
    • 67650506868 scopus 로고    scopus 로고
    • Stochastic phase reduction for a general class of noisy limit cycle oscillators
    • J.N. Teramae, H. Nakao, and G.B. Ermentrout Stochastic phase reduction for a general class of noisy limit cycle oscillators Phys. Rev. Lett. 102 2009 194102
    • (2009) Phys. Rev. Lett. , vol.102 , pp. 194102
    • Teramae, J.N.1    Nakao, H.2    Ermentrout, G.B.3
  • 23
    • 54049109601 scopus 로고    scopus 로고
    • Phase reduction of stochastic limit cycle oscillators
    • K. Yoshimura, and K. Arai Phase reduction of stochastic limit cycle oscillators Phys. Rev. Lett. 101 2008 154101
    • (2008) Phys. Rev. Lett. , vol.101 , pp. 154101
    • Yoshimura, K.1    Arai, K.2
  • 24
    • 0037011709 scopus 로고    scopus 로고
    • Noise-induced transport with low randomness
    • B. Lindner, and L. Schimansky-Geier Noise-induced transport with low randomness Phys. Rev. Lett. 89 2002 230602
    • (2002) Phys. Rev. Lett. , vol.89 , pp. 230602
    • Lindner, B.1    Schimansky-Geier, L.2
  • 25
    • 84990947014 scopus 로고    scopus 로고
    • Evaluation of entrainment of a nonlinear neural oscillator to white noise
    • J. Ritt Evaluation of entrainment of a nonlinear neural oscillator to white noise Phys. Rev. E 68 2003 41915
    • (2003) Phys. Rev. e , vol.68 , pp. 41915
    • Ritt, J.1
  • 26
    • 43049096471 scopus 로고    scopus 로고
    • Class-II neurons display a higher degree of stochastic synchronization than class-I neurons
    • S. Marella, and G.B. Ermentrout Class-II neurons display a higher degree of stochastic synchronization than class-I neurons Phys. Rev. E 77 2008 41918
    • (2008) Phys. Rev. e , vol.77 , pp. 41918
    • Marella, S.1    Ermentrout, G.B.2
  • 27
    • 65049086630 scopus 로고    scopus 로고
    • Synchronization dynamics of two coupled neural oscillators receiving shared and unshared noisy stimuli
    • C. Ly, and G.B. Ermentrout Synchronization dynamics of two coupled neural oscillators receiving shared and unshared noisy stimuli J. Comput. Neurosci. 26 2009 425 443
    • (2009) J. Comput. Neurosci. , vol.26 , pp. 425-443
    • Ly, C.1    Ermentrout, G.B.2
  • 28
    • 0043009735 scopus 로고    scopus 로고
    • Analytic expressions for rate and CV of a type I neuron driven by white gaussian noise
    • B. Lindner, A. Longtin, and A. Bulsara Analytic expressions for rate and CV of a type I neuron driven by white Gaussian noise Neural Comput. 15 2003 1761 1788 (Pubitemid 37035547)
    • (2003) Neural Computation , vol.15 , Issue.8 , pp. 1761-1788
    • Lindner, B.1    Longtin, A.2    Bulsara, A.3
  • 29
    • 0033859101 scopus 로고    scopus 로고
    • Temporal processing in sensory systems
    • DOI 10.1016/S0959-4388(00)00115-X
    • B. Grothe, and G. Klump Temporal processing in sensory systems Curr. Opin. Neurobiology 10 2000 467 473 (Pubitemid 30614506)
    • (2000) Current Opinion in Neurobiology , vol.10 , Issue.4 , pp. 467-473
    • Grothe, B.1    Klump, G.M.2
  • 30
    • 0035707111 scopus 로고    scopus 로고
    • Temporal and rate representations of time-varying signals in the auditory cortex of awake primates
    • DOI 10.1038/nn737
    • T. Lu, L. Liang, and X. Wang Temporal and rate representations of time-varying signals in the auditory cortex of awake primates Nature Neurosci. 4 2001 1131 1138 (Pubitemid 34116559)
    • (2001) Nature Neuroscience , vol.4 , Issue.11 , pp. 1131-1138
    • Lu, T.1    Liang, L.2    Wang, X.3
  • 31
    • 39449119804 scopus 로고    scopus 로고
    • Embodied Information Processing: Vibrissa Mechanics and Texture Features Shape Micromotions in Actively Sensing Rats
    • DOI 10.1016/j.neuron.2007.12.024, PII S0896627308000275
    • J. Ritt, M. Andermann, and C. Moore Embodied information processing: vibrissa mechanics and texture features shape micromotions in actively sensing rats Neuron 57 2008 599 613 (Pubitemid 351273990)
    • (2008) Neuron , vol.57 , Issue.4 , pp. 599-613
    • Ritt, J.T.1    Andermann, M.L.2    Moore, C.I.3
  • 32
    • 0005483993 scopus 로고
    • The Volterra representation and the Wiener expansion: Validity and pitfalls
    • G. Palm, and T. Poggio The Volterra representation and the Wiener expansion: validity and pitfalls SIAM J. Appl. Math. 1977 195 216
    • (1977) SIAM J. Appl. Math. , pp. 195-216
    • Palm, G.1    Poggio, T.2
  • 34
    • 0019405994 scopus 로고
    • Voltage oscillations in the barnacle giant muscle fiber
    • C. Morris, and H. Lecar Voltage oscillations in the barnacle giant muscle fiber Biophys. J. 193 1981 193 213 (Pubitemid 11079105)
    • (1981) Biophysical Journal , vol.35 , Issue.1 , pp. 193-213
    • Morris, C.1    Lecar, H.2
  • 35
    • 0031929324 scopus 로고    scopus 로고
    • Analytical and simulation results for stochastic Fitzhugh-Nagumo neurons and neural networks
    • DOI 10.1023/A:1008811814446
    • H. Tuckwell, and R. Rodriguez Analytical and simulation results for stochastic FitzhughNagumo neurons and neural networks J. Comput. Neurosci. 5 1998 91 113 (Pubitemid 28105079)
    • (1998) Journal of Computational Neuroscience , vol.5 , Issue.1 , pp. 91-113
    • Tuckwell, H.C.1    Rodriguez, R.2
  • 36
    • 0032212602 scopus 로고    scopus 로고
    • Noisy spiking neurons and networks: Useful approximations for firing probabilities and global behavior
    • DOI 10.1016/S0303-2647(98)00065-3, PII S0303264798000653
    • R. Rodriguez, and H. Tuckwell Noisy spiking neurons and networks: useful approximations for firing probabilities and global behavior Biosystems 48 1998 187 194 (Pubitemid 28526577)
    • (1998) BioSystems , vol.48 , Issue.1-3 , pp. 187-194
    • Rodriguez, R.1    C. Tuckwell, H.2
  • 38
    • 34247893807 scopus 로고    scopus 로고
    • Noise-induced synchronization and clustering in ensembles of uncoupled limit-cycle oscillators
    • H. Nakao, K. Arai, and Y. Kawamura Noise-induced synchronization and clustering in ensembles of uncoupled limit-cycle oscillators Phys. Rev. Lett. 98 2007 184101
    • (2007) Phys. Rev. Lett. , vol.98 , pp. 184101
    • Nakao, H.1    Arai, K.2    Kawamura, Y.3
  • 39
    • 36849103164 scopus 로고
    • On symmetry-breaking instabilities in dissipative systems
    • I. Prigogine, and G. Nicolis On symmetry-breaking instabilities in dissipative systems J. Chem. Phys. 46 1967 3542
    • (1967) J. Chem. Phys. , vol.46 , pp. 3542
    • Prigogine, I.1    Nicolis, G.2
  • 40
    • 0016314153 scopus 로고
    • Isochrons and phaseless sets
    • J. Guckenheimer Isochrons and phaseless sets J. Math. Biol. 1 1975 259 273
    • (1975) J. Math. Biol. , vol.1 , pp. 259-273
    • Guckenheimer, J.1
  • 41
    • 0016194585 scopus 로고
    • Patterns of phase compromise in biological cycles
    • A.T. Winfree Patterns of phase compromise in biological cycles J. Math. Biol. 1 1974 73 93
    • (1974) J. Math. Biol. , vol.1 , pp. 73-93
    • Winfree, A.T.1
  • 42
    • 0030195232 scopus 로고    scopus 로고
    • Type i membranes, phase-resetting curves, and synchrony
    • G.B. Ermentrout Type I membranes, phase-resetting curves, and synchrony Neural Comput. 8 1996 979 1001
    • (1996) Neural Comput. , vol.8 , pp. 979-1001
    • Ermentrout, G.B.1
  • 43
    • 0033645566 scopus 로고    scopus 로고
    • Phase equations for relaxation oscillators
    • E. Izhikevich Phase equations for relaxation oscillators SIAM J. Appl. Math. 60 2000 1789 1804
    • (2000) SIAM J. Appl. Math. , vol.60 , pp. 1789-1804
    • Izhikevich, E.1
  • 44
    • 1542351229 scopus 로고    scopus 로고
    • On the Phase Reduction and Response Dynamics of Neural Oscillator Populations
    • DOI 10.1162/089976604322860668
    • E. Brown, J. Moehlis, and P. Holmes On the phase reduction and response dynamics of neural oscillator populations Neural Comput. 16 2004 673 715 (Pubitemid 38318129)
    • (2004) Neural Computation , vol.16 , Issue.4 , pp. 673-715
    • Brown, E.1    Moehlis, J.2    Holmes, P.3
  • 48
    • 0014109171 scopus 로고
    • Neuronal spike trains and stochastic point processes. I: The single spike train
    • D. Perkel, G. Gerstein, and G. Moore Neuronal spike trains and stochastic point processes. I: the single spike train J. Biophys. 7 1967 391 418
    • (1967) J. Biophys. , vol.7 , pp. 391-418
    • Perkel, D.1    Gerstein, G.2    Moore, G.3
  • 49
    • 0014104894 scopus 로고
    • Neuronal spike trains and stochastic point processes. II: Simultaneous spike trains
    • D. Perkel, G. Gerstein, and G. Moore Neuronal spike trains and stochastic point processes. II: simultaneous spike trains J. Biophys. 7 1967 419 440
    • (1967) J. Biophys. , vol.7 , pp. 419-440
    • Perkel, D.1    Gerstein, G.2    Moore, G.3
  • 50
    • 36749062075 scopus 로고    scopus 로고
    • The spikes trains probability distributions: A stochastic calculus approach
    • DOI 10.1016/j.jphysparis.2007.10.008, PII S0928425707000393, Neuro-Computation: From Sensorimotor Integration to Computational Frameworks
    • J. Touboul, and O. Faugeras The spikes trains probability distributions: a stochastic calculus approach J. Phys. (Paris) 101 2007 78 98 (Pubitemid 350214515)
    • (2007) Journal of Physiology Paris , vol.101 , Issue.1-3 , pp. 78-98
    • Touboul, J.1    Faugeras, O.2
  • 51
    • 76149139425 scopus 로고    scopus 로고
    • Coupling regularizes individual units in noisy populations
    • C. Ly, and G. Ermentrout Coupling regularizes individual units in noisy populations Phys. Rev. E 81 2010 011911
    • (2010) Phys. Rev. e , vol.81 , pp. 011911
    • Ly, C.1    Ermentrout, G.2
  • 52
    • 77951994800 scopus 로고    scopus 로고
    • Relative spike timing in stochastic oscillator networks of the Hermissenda eye
    • W. Nesse, and G. Clark Relative spike timing in stochastic oscillator networks of the Hermissenda eye Biol. Cybernet. 102 2010 389 412
    • (2010) Biol. Cybernet. , vol.102 , pp. 389-412
    • Nesse, W.1    Clark, G.2
  • 53
    • 79951515785 scopus 로고    scopus 로고
    • Analysis of recurrent networks of pulse-coupled noisy neural oscillators
    • C. Ly, and G.B. Ermentrout Analysis of recurrent networks of pulse-coupled noisy neural oscillators SIAM J. Appl. Dyn. Syst. 9 2010 113 137
    • (2010) SIAM J. Appl. Dyn. Syst. , vol.9 , pp. 113-137
    • Ly, C.1    Ermentrout, G.B.2
  • 54
    • 0034076273 scopus 로고    scopus 로고
    • A population density approach that facilitates large-scale modeling of neural networks: Analysis and an application to orientation tuning
    • DOI 10.1023/A:1008912914816
    • D.Q. Nykamp, and D. Tranchina A population density approach that facilitates large-scale modeling of neural networks: analysis and an application to orientation tuning J. Comput. Neurosci. 8 2000 19 50 (Pubitemid 30201219)
    • (2000) Journal of Computational Neuroscience , vol.8 , Issue.1 , pp. 19-50
    • Nykamp, D.Q.1    Tranchina, D.2
  • 55
    • 65049084636 scopus 로고    scopus 로고
    • A finite volume method for stochastic integrate-and-fire models
    • F. Marpeau, A. Barua, and K. Josi A finite volume method for stochastic integrate-and-fire models J. Comput. Neurosci. 26 2009 445 457
    • (2009) J. Comput. Neurosci. , vol.26 , pp. 445-457
    • Marpeau, F.1    Barua, A.2    Josi, K.3
  • 56
    • 0020471747 scopus 로고
    • Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: A theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias
    • DOI 10.1007/BF02154750
    • M. Guevara, and L. Glass Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: a theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias J. Math. Biol. 14 1982 1 23 (Pubitemid 12120075)
    • (1982) Journal of Mathematical Biology , vol.14 , Issue.1 , pp. 1-23
    • Guevara, M.R.1    Glass, L.2
  • 58
    • 0015353310 scopus 로고
    • The relationship between the firing rate of a single neuron and the level of activity in a population of neurons. Experimental evidence for resonant enhancement in the population response
    • B.W. Knight The relationship between the firing rate of a single neuron and the level of activity in a population of neurons. Experimental evidence for resonant enhancement in the population response J. Gen. Physiol. 59 1972 767 778
    • (1972) J. Gen. Physiol. , vol.59 , pp. 767-778
    • Knight, B.W.1
  • 59
    • 0034153464 scopus 로고    scopus 로고
    • Dynamics of encoding in neuron populations: Some general mathematical features
    • B.W. Knight Dynamics of encoding in neuron populations: some general mathematical features Neural Comput. 12 2000 473 518
    • (2000) Neural Comput. , vol.12 , pp. 473-518
    • Knight, B.W.1
  • 61
    • 0024433313 scopus 로고
    • How the ear's works work
    • DOI 10.1038/341397a0
    • A. Hudspeth How the ear's works work Nature 341 1989 397 404 (Pubitemid 19241904)
    • (1989) Nature , vol.341 , Issue.6241 , pp. 397-404
    • Hudspeth, A.J.1


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