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Volumn 34, Issue 5, 2008, Pages 521-538

Stochastic hierarchical systems: Excitable dynamics

Author keywords

Delayed integral equations; Excitable systems; Time convoluted master equations

Indexed keywords

ION CHANNEL; VOLTAGE DEPENDENT ANION CHANNEL;

EID: 56649095818     PISSN: 00920606     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10867-008-9112-1     Document Type: Article
Times cited : (2)

References (66)
  • 3
    • 0000700033 scopus 로고
    • Transport-properties of the continuous-time random-walk with a long-tailed waiting-time density
    • H. Weissman G.H. Weiss S. Havlin 1989 Transport-properties of the continuous-time random-walk with a long-tailed waiting-time density J. Stat. Phys. 57 301 317
    • (1989) J. Stat. Phys. , vol.57 , pp. 301-317
    • Weissman, H.1    Weiss, G.H.2    Havlin, S.3
  • 4
    • 24444433584 scopus 로고
    • Nonequilibrium dynamics of spin glasses
    • D.S. Fisher D.A. Huse 1988 Nonequilibrium dynamics of spin glasses Phys. Rev. B 38 373 385
    • (1988) Phys. Rev. B , vol.38 , pp. 373-385
    • Fisher, D.S.1    Huse, D.A.2
  • 5
    • 0037060212 scopus 로고    scopus 로고
    • Waiting-time statistics of self-organized-criticality systems
    • R. Sànchez D.E. Newman B.A. Carreras 2002 Waiting-time statistics of self-organized-criticality systems Phys. Rev. Lett. 88 068302
    • (2002) Phys. Rev. Lett. , vol.88 , pp. 068302
    • Sànchez, R.1    Newman, D.E.2    Carreras, B.A.3
  • 6
    • 41349083937 scopus 로고    scopus 로고
    • Non-Markovian random processes and traveling fronts in a reaction-transport system with memory and long-range interactions
    • S. Fedotov Y. Okuda 2002 Non-Markovian random processes and traveling fronts in a reaction-transport system with memory and long-range interactions Phys. Rev. E 66 021113
    • (2002) Phys. Rev. e , vol.66 , pp. 021113
    • Fedotov, S.1    Okuda, Y.2
  • 7
    • 34250415771 scopus 로고
    • Asymptotic solutions of continuous-time random walks
    • M.F. Shlesinger 1974 Asymptotic solutions of continuous-time random walks J. Stat Phys. 10 421 434
    • (1974) J. Stat Phys. , vol.10 , pp. 421-434
    • Shlesinger, M.F.1
  • 8
    • 0040457675 scopus 로고
    • Excess noise in a hopping model for a resistor with quenched disorder
    • Th.M. Nieuwenhuizen M.H. Ernst 1985 Excess noise in a hopping model for a resistor with quenched disorder J. Stat. Phys. 41 773 801
    • (1985) J. Stat. Phys. , vol.41 , pp. 773-801
    • Nieuwenhuizen, Th.M.1    Ernst, M.H.2
  • 9
    • 4243202118 scopus 로고
    • Waiting times for random walks on regular and fractal lattices
    • C. Van den Broeck 1989 Waiting times for random walks on regular and fractal lattices Phys. Rev. Lett. 62 1421 1424
    • (1989) Phys. Rev. Lett. , vol.62 , pp. 1421-1424
    • Van Den Broeck, C.1
  • 15
    • 3142773575 scopus 로고    scopus 로고
    • Reading the patterns in living cells - The physics of Ca2+ signaling
    • M. Falcke 2004 Reading the patterns in living cells - the physics of Ca2+ signaling Adv. Phys. 53 255 440
    • (2004) Adv. Phys. , vol.53 , pp. 255-440
    • Falcke, M.1
  • 16
    • 0029374551 scopus 로고
    • Spontaneous excitations in the visual-cortex - Stripes, spirals, rings, and collective bursts
    • C. Fohlmeister R. Ritz W. Gerstner J.L. van Hemmen 1995 Spontaneous excitations in the visual-cortex - stripes, spirals, rings, and collective bursts Neural Comput. 7 905 914
    • (1995) Neural Comput. , vol.7 , pp. 905-914
    • Fohlmeister, C.1    Ritz, R.2    Gerstner, W.3    Van Hemmen, J.L.4
  • 20
    • 0039806342 scopus 로고    scopus 로고
    • The sound of many hands clapping - Tumultuous applause can transform itself into waves of synchronized clapping
    • Z. Néda E. Ravasz Y. Brechet T. Vicsek A.L. Barabási 2000 The sound of many hands clapping - Tumultuous applause can transform itself into waves of synchronized clapping Nature (London) 403 849 850
    • (2000) Nature (London) , vol.403 , pp. 849-850
    • Néda, Z.1    Ravasz, E.2    Brechet, Y.3    Vicsek, T.4    Barabási, A.L.5
  • 21
    • 0035490101 scopus 로고    scopus 로고
    • Dynamic predictions: Oscillations and synchrony in top-down processing
    • A.K. Engel P. Fries W. Singer 2001 Dynamic predictions: oscillations and synchrony in top-down processing Nature Rev. Neurosci. 2 704 716
    • (2001) Nature Rev. Neurosci. , vol.2 , pp. 704-716
    • Engel, A.K.1    Fries, P.2    Singer, W.3
  • 23
    • 4043099181 scopus 로고    scopus 로고
    • Abrupt glacial climate changes due to stochastic resonance
    • A. Ganopolski S. Rahmstorf 2002 Abrupt glacial climate changes due to stochastic resonance Phys. Rev. Lett. 88 038501
    • (2002) Phys. Rev. Lett. , vol.88 , pp. 038501
    • Ganopolski, A.1    Rahmstorf, S.2
  • 24
    • 0032111678 scopus 로고    scopus 로고
    • Dynamics of membrane excitability determine interspike interval variability: A link between spike generation mechanisms and cortical spike train statistics
    • B.S. Gutkin G.B. Ermentrout 1998 Dynamics of membrane excitability determine interspike interval variability: a link between spike generation mechanisms and cortical spike train statistics Neural Comput. 10 1047 1065
    • (1998) Neural Comput. , vol.10 , pp. 1047-1065
    • Gutkin, B.S.1    Ermentrout, G.B.2
  • 26
    • 84956515648 scopus 로고
    • The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle
    • N. Wiener A. Rosenbluth 1946 The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle Arch. Inst. Cardiol. Mex. 16 205 265
    • (1946) Arch. Inst. Cardiol. Mex. , vol.16 , pp. 205-265
    • Wiener, N.1    Rosenbluth, A.2
  • 27
    • 5944229562 scopus 로고
    • Spatiotemporal stochastic resonance in excitable media
    • P. Jung G. Mayer-Kress 1995 Spatiotemporal stochastic resonance in excitable media Phys. Rev. Lett. 74 2130 2133
    • (1995) Phys. Rev. Lett. , vol.74 , pp. 2130-2133
    • Jung, P.1    Mayer-Kress, G.2
  • 29
    • 0037671497 scopus 로고    scopus 로고
    • Statistics of entrance times
    • P. Talkner 2003 Statistics of entrance times Physica A 325 124 135
    • (2003) Physica a , vol.325 , pp. 124-135
    • Talkner, P.1
  • 31
    • 4344670146 scopus 로고    scopus 로고
    • Firing time statistics for driven neuron models: Analytic expressions versus numerics
    • M. Schindler P. Talkner P. Hänggi 2004 Firing time statistics for driven neuron models: analytic expressions versus numerics Phys. Rev. Lett. 93 048102
    • (2004) Phys. Rev. Lett. , vol.93 , pp. 048102
    • Schindler, M.1    Talkner, P.2    Hänggi, P.3
  • 33
    • 79051470670 scopus 로고    scopus 로고
    • Waiting time distributions for cluster of complex molecules
    • R. Thul M. Falcke 2007 Waiting time distributions for cluster of complex molecules Europhys Lett. 79 38003
    • (2007) Europhys Lett. , vol.79 , pp. 38003
    • Thul, R.1    Falcke, M.2
  • 36
    • 0014108715 scopus 로고
    • Biological rhythms and behavior of populations of coupled oscillators
    • A.T. Winfree 1967 Biological rhythms and behavior of populations of coupled oscillators J. Theor. Biol. 16 15 42
    • (1967) J. Theor. Biol. , vol.16 , pp. 15-42
    • Winfree, A.T.1
  • 37
    • 0014838120 scopus 로고
    • Integrated view resetting a circadian clock
    • A.T. Winfree 1970 Integrated view resetting a circadian clock J. Theor. Biol. 28 327 374
    • (1970) J. Theor. Biol. , vol.28 , pp. 327-374
    • Winfree, A.T.1
  • 39
    • 0039592729 scopus 로고    scopus 로고
    • From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators
    • S.H. Strogatz 2000 From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators Physica D 143 1 20
    • (2000) Physica D , vol.143 , pp. 1-20
    • Strogatz, S.H.1
  • 42
    • 0347947148 scopus 로고    scopus 로고
    • Stochastic resonance in a non-Markovian discrete state model for excitable systems
    • T. Prager L. Schimansky-Geier 2003 Stochastic resonance in a non-Markovian discrete state model for excitable systems Phys. Rev. Lett. 91 230601
    • (2003) Phys. Rev. Lett. , vol.91 , pp. 230601
    • Prager, T.1    Schimansky-Geier, L.2
  • 43
    • 37649026666 scopus 로고    scopus 로고
    • Phase velocity and phase diffusion in periodically driven discrete-state systems
    • T. Prager L. Schimansky-Geier 2005 Phase velocity and phase diffusion in periodically driven discrete-state systems Phys. Rev. E. 71 031112
    • (2005) Phys. Rev. E. , vol.71 , pp. 031112
    • Prager, T.1    Schimansky-Geier, L.2
  • 44
    • 0001723799 scopus 로고
    • Phase transitions in active rotator systems
    • S. Shinomoto Y. Kuramoto 1986 Phase transitions in active rotator systems Progr. Theor. Phys. 75 1105 1110
    • (1986) Progr. Theor. Phys. , vol.75 , pp. 1105-1110
    • Shinomoto, S.1    Kuramoto, Y.2
  • 45
    • 0001527148 scopus 로고
    • Phase-transitions and their bifurcation-analysis in a large population of active rotators with mean-field coupling
    • H. Sakaguchi S. Shinomoto Y. Kuramoto 1988 Phase-transitions and their bifurcation-analysis in a large population of active rotators with mean-field coupling Progr. Theor. Phys. 79 600 607
    • (1988) Progr. Theor. Phys. , vol.79 , pp. 600-607
    • Sakaguchi, H.1    Shinomoto, S.2    Kuramoto, Y.3
  • 46
    • 0000241637 scopus 로고    scopus 로고
    • Noise-sustained pulsating patterns and global oscillations in subexcitable media
    • H. Hempel L. Schimansky-Geier J. García-Ojalvo 1999 Noise-sustained pulsating patterns and global oscillations in subexcitable media Phys. Rev. Lett. 82 3713 3716
    • (1999) Phys. Rev. Lett. , vol.82 , pp. 3713-3716
    • Hempel, H.1    Schimansky-Geier, L.2    García-Ojalvo, J.3
  • 48
    • 0000349482 scopus 로고    scopus 로고
    • Phase synchronization in coupled nonidentical excitable systems and array-enhanced coherence resonance
    • B. Hu C.S. Zhou 2000 Phase synchronization in coupled nonidentical excitable systems and array-enhanced coherence resonance Phys. Rev. E 61 R1001 R1004
    • (2000) Phys. Rev. e , vol.61
    • Hu, B.1    Zhou, C.S.2
  • 49
    • 0035959211 scopus 로고    scopus 로고
    • Array-enhanced coherence resonance: Nontrivial effects of heterogeneity and spatial independence of noise
    • C. Zhou J. Kurths B. Hu 2001 Array-enhanced coherence resonance: nontrivial effects of heterogeneity and spatial independence of noise Phys. Rev. Lett. 87 098101
    • (2001) Phys. Rev. Lett. , vol.87 , pp. 098101
    • Zhou, C.1    Kurths, J.2    Hu, B.3
  • 50
    • 37649031330 scopus 로고    scopus 로고
    • Collective dynamics of two-mode stochastic oscillators
    • A. Nikitin Z. Néda T. Vicsek 2001 Collective dynamics of two-mode stochastic oscillators Phys. Rev. Lett. 87 024101
    • (2001) Phys. Rev. Lett. , vol.87 , pp. 024101
    • Nikitin, A.1    Néda, Z.2    Vicsek, T.3
  • 51
    • 0037493668 scopus 로고    scopus 로고
    • Influence of spatiotemporally correlated noise on structure formation in excitable media
    • H. Busch F. Kaiser 2003 Influence of spatiotemporally correlated noise on structure formation in excitable media Phys. Rev. E 67 041105
    • (2003) Phys. Rev. e , vol.67 , pp. 041105
    • Busch, H.1    Kaiser, F.2
  • 52
    • 1442354867 scopus 로고    scopus 로고
    • Noise-controlled oscillations and their bifurcations in coupled phase oscillators
    • M.A. Zaks A.B. Neiman S. Feistel L. Schimansky-Geier 2003 Noise-controlled oscillations and their bifurcations in coupled phase oscillators Phys. Rev. E 68 066206
    • (2003) Phys. Rev. e , vol.68 , pp. 066206
    • Zaks, M.A.1    Neiman, A.B.2    Feistel, S.3    Schimansky-Geier, L.4
  • 53
    • 0022524005 scopus 로고
    • Influence of noise on Duffing - Van der Pol oscillators
    • W. Ebeling H. Herzel W. Richert L. Schimansky-Geier 1986 Influence of noise on Duffing - van der Pol oscillators ZAMM 66 141 146
    • (1986) ZAMM , vol.66 , pp. 141-146
    • Ebeling, W.1    Herzel, H.2    Richert, W.3    Schimansky-Geier, L.4
  • 54
    • 0021445898 scopus 로고
    • Noise induced limit cycles of the Bonhoeffer-Van der Pol model of neural pulses
    • H. Treutlein K. Schulten 1985 Noise induced limit cycles of the Bonhoeffer-Van der Pol model of neural pulses Ber. Bunsenges. Phys. Chem. 89 710 718
    • (1985) Ber. Bunsenges. Phys. Chem. , vol.89 , pp. 710-718
    • Treutlein, H.1    Schulten, K.2
  • 55
    • 0000873649 scopus 로고
    • Pseudo-regular oscillations induced by external noise
    • D. Sigeti W. Horsthemke 1989 Pseudo-regular oscillations induced by external noise J. Stat. Phys. 54 1217 1222
    • (1989) J. Stat. Phys. , vol.54 , pp. 1217-1222
    • Sigeti, D.1    Horsthemke, W.2
  • 57
    • 0000912646 scopus 로고    scopus 로고
    • Coherence resonance in a noise-driven excitable system
    • A.S. Pikovsky J. Kurths 1997 Coherence resonance in a noise-driven excitable system Phys. Rev. Lett. 78 775 778
    • (1997) Phys. Rev. Lett. , vol.78 , pp. 775-778
    • Pikovsky, A.S.1    Kurths, J.2
  • 58
    • 85032428354 scopus 로고    scopus 로고
    • Controlling synchronization in an ensemble of globally coupled oscillators
    • M.G. Rosenblum A.S. Pikovsky 2004 Controlling synchronization in an ensemble of globally coupled oscillators Phys. Rev. Lett. 92 114102
    • (2004) Phys. Rev. Lett. , vol.92 , pp. 114102
    • Rosenblum, M.G.1    Pikovsky, A.S.2
  • 59
    • 31144434673 scopus 로고    scopus 로고
    • Noise-induced complexity: From subthreshold oscillations to spiking in coupled excitable systems
    • M.A. Zaks X. Sailer L. Schimansky-Geier A. Neiman 2005 Noise-induced complexity: from subthreshold oscillations to spiking in coupled excitable systems Chaos 15 026117
    • (2005) Chaos , vol.15 , pp. 026117
    • Zaks, M.A.1    Sailer, X.2    Schimansky-Geier, L.3    Neiman, A.4
  • 60
    • 0030124574 scopus 로고    scopus 로고
    • Noise-induced phase transitions in globally coupled active rotators
    • S.H. Park S. Kim 1996 Noise-induced phase transitions in globally coupled active rotators Phys. Rev. E 53 3425 3430
    • (1996) Phys. Rev. e , vol.53 , pp. 3425-3430
    • Park, S.H.1    Kim, S.2
  • 61
    • 41349102500 scopus 로고    scopus 로고
    • Cooperative dynamics in a network of stochastic elements with delayed feedback
    • D. Huber L.S. Tsimring 2005 Cooperative dynamics in a network of stochastic elements with delayed feedback Phys. Rev. E 71 036150
    • (2005) Phys. Rev. e , vol.71 , pp. 036150
    • Huber, D.1    Tsimring, L.S.2
  • 62
    • 23444438881 scopus 로고    scopus 로고
    • Mean-field approximation of time-delayed feedback control of noise-induced oscillations in the Van der Pol system
    • J. Pomplun A. Amann E. Schöll 2005 Mean-field approximation of time-delayed feedback control of noise-induced oscillations in the Van der Pol system Europhys. Lett. 71 366 372
    • (2005) Europhys. Lett. , vol.71 , pp. 366-372
    • Pomplun, J.1    Amann, A.2    Schöll, E.3
  • 63
    • 45849154659 scopus 로고    scopus 로고
    • Noise-induced dynamics in bistable systems with delay
    • L.S. Tsimring A.S. Pikovsky 2001 Noise-induced dynamics in bistable systems with delay Phys. Rev. Lett. 87 250602
    • (2001) Phys. Rev. Lett. , vol.87 , pp. 250602
    • Tsimring, L.S.1    Pikovsky, A.S.2
  • 64
    • 1042300689 scopus 로고    scopus 로고
    • Dynamics of an ensemble of noisy bistable elements with global time delayed coupling
    • D. Huber L.S. Tsimring 2003 Dynamics of an ensemble of noisy bistable elements with global time delayed coupling Phys. Rev. Lett. 91 206601
    • (2003) Phys. Rev. Lett. , vol.91 , pp. 206601
    • Huber, D.1    Tsimring, L.S.2
  • 65
    • 0000068964 scopus 로고    scopus 로고
    • Time delay induced death in coupled limit cycle oscillators
    • D.V.R. Reddy A. Sen G.L. Johnston 1998 Time delay induced death in coupled limit cycle oscillators Phys. Rev. Lett. 80 5109 5112
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 5109-5112
    • Reddy, D.V.R.1    Sen, A.2    Johnston, G.L.3
  • 66
    • 33646530989 scopus 로고    scopus 로고
    • Drift and diffusion in periodically driven renewal processes
    • T. Prager L. Schimansky-Geier 2006 Drift and diffusion in periodically driven renewal processes J. Stat. Phys. 123 391 413
    • (2006) J. Stat. Phys. , vol.123 , pp. 391-413
    • Prager, T.1    Schimansky-Geier, L.2


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