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Generation of slow phase-locked oscillation and variability of the interspike intervals in globally coupled neuronal oscillators
1. | Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan, Japan |
2. | Faculty of Human Relation, Kyoto Koka Women's University, Kyoto 615-0882, Japan |
References:
[1] |
R. Borisyuk, D. Chik and Y. Kazanovich, Visual perception of ambiguous figures: Synchronization based neural models, Biol. Cybern., 100 (2009), 491-504.
doi: 10.1007/s00422-009-0301-1. |
[2] |
L. Cheng and B. Ermentrout, Analytic approximations of statistical quantities and response of noisy oscillators, Physica D, 240 (2011), 719-731. |
[3] |
H. Daido, Why circadian rhythms are circadian: Competitive population dynamics of biological oscillators, Phys. Rev. Lett., 87 (2001), 048101.
doi: 10.1103/PhysRevLett.87.048101. |
[4] |
E. J. Doedel and B. E. Oldeman, et al., AUTO-07P: Continuation and bifurcation software for ordinary differential equations, Concordia University, 2009. |
[5] |
S. Doi and J. Inoue, Chaos and variability of inter-spike intervals in neuronal models with slow-fast dynamics, AIP Conf. Proc., 1339 (2011), 210-221. |
[6] |
S. Doi and S. Kumagai, Generation of very slow neuronal rhythms and chaos near the Hopf bifurcation in single neuron models, J. Comp. Neurosci., 19 (2005), 325-356.
doi: 10.1007/s10827-005-2895-1. |
[7] |
S. Doi and S. Sato, Regulation of differentiation in a population of cells interacting through a common pool, J. Math. Biol., 26 (1988), 435-454.
doi: 10.1007/BF00276372. |
[8] |
B. Ermentrout and M. Wechselberger, Canards, clusters, and synchronization in a weakly coupled interneuron model, SIAM J. Appl. Dyn. Syst., 8 (2009), 253-278.
doi: 10.1137/080724010. |
[9] |
R. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane, Biophy. J., 1 (1961), 445-466.
doi: 10.1016/S0006-3495(61)86902-6. |
[10] |
L. Glass, Synchronization and rhythmic processes in physiology, Nature, 410 (2001), 277-284.
doi: 10.1038/35065745. |
[11] |
B. Gutkin and B. Ermentrout, Dynamics of membrane excitability determine interspike interval variability: A link between spike generation mechanisms and cortical spike train statistics, Neural Comput., 10 (1998), 1047-1065.
doi: 10.1162/089976698300017331. |
[12] |
B. Gutkin, J. Jost and H. Tuckwell, Inhibition of rhythmic neural spiking by noise: The occurrence of a minimum in activity with increasing noise, Naturwiss., 96 (2009), 1091-1097.
doi: 10.1007/s00114-009-0570-5. |
[13] |
A. L. Hodgkin and A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol., 117 (1952), 500-544. |
[14] |
J. Honerkamp, G. Mutschler and R. Seitz, Coupling of a slow and a fast oscillator can generate bursting, Bull. Math. Biol., 47 (1985), 1-21.
doi: 10.1016/S0092-8240(85)90002-3. |
[15] |
G. Katriel, Synchronization of oscillators coupled through an environment, Physica D, 237 (2008), 2933-2944.
doi: 10.1016/j.physd.2008.04.015. |
[16] |
H. Kori, Y. Kawamura and N. Masuda, Structure of cell networks critically determines oscillation regularity, J. Theor. Biol., 297 (2012), 61-72.
doi: 10.1016/j.jtbi.2011.12.007. |
[17] |
Y. Kuramoto, "Chemical Oscillations, Waves, and Turbulence," Springer Series in Synergetics, 19, Springer-Verlag, Berlin, 1984.
doi: 10.1007/978-3-642-69689-3. |
[18] |
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.
doi: 10.1162/08997660360675035. |
[19] |
J. Nagumo, S. Arimoto and S. Yoshizawa, An active pulse transmission line simulating nerve axon, Proc. IRE, 50 (1962), 2061-2070.
doi: 10.1109/JRPROC.1962.288235. |
[20] |
A. Pikovsky, M. Rosenblum and J. Kurths, "Synchronization: A Universal Concept in Nonlinear Sciences," Cambridge Nonlinear Science Series, 12, Cambridge University Press, Cambridge, 2001.
doi: 10.1017/CBO9780511755743. |
[21] |
K. Sugimoto, Y. Nii, S. Doi and S. Kumagai, Frequency variability of neural rhythm in a small network of pacemaker neurons, Proc. of AROB 7th '02, (2002), 54-57. |
show all references
References:
[1] |
R. Borisyuk, D. Chik and Y. Kazanovich, Visual perception of ambiguous figures: Synchronization based neural models, Biol. Cybern., 100 (2009), 491-504.
doi: 10.1007/s00422-009-0301-1. |
[2] |
L. Cheng and B. Ermentrout, Analytic approximations of statistical quantities and response of noisy oscillators, Physica D, 240 (2011), 719-731. |
[3] |
H. Daido, Why circadian rhythms are circadian: Competitive population dynamics of biological oscillators, Phys. Rev. Lett., 87 (2001), 048101.
doi: 10.1103/PhysRevLett.87.048101. |
[4] |
E. J. Doedel and B. E. Oldeman, et al., AUTO-07P: Continuation and bifurcation software for ordinary differential equations, Concordia University, 2009. |
[5] |
S. Doi and J. Inoue, Chaos and variability of inter-spike intervals in neuronal models with slow-fast dynamics, AIP Conf. Proc., 1339 (2011), 210-221. |
[6] |
S. Doi and S. Kumagai, Generation of very slow neuronal rhythms and chaos near the Hopf bifurcation in single neuron models, J. Comp. Neurosci., 19 (2005), 325-356.
doi: 10.1007/s10827-005-2895-1. |
[7] |
S. Doi and S. Sato, Regulation of differentiation in a population of cells interacting through a common pool, J. Math. Biol., 26 (1988), 435-454.
doi: 10.1007/BF00276372. |
[8] |
B. Ermentrout and M. Wechselberger, Canards, clusters, and synchronization in a weakly coupled interneuron model, SIAM J. Appl. Dyn. Syst., 8 (2009), 253-278.
doi: 10.1137/080724010. |
[9] |
R. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane, Biophy. J., 1 (1961), 445-466.
doi: 10.1016/S0006-3495(61)86902-6. |
[10] |
L. Glass, Synchronization and rhythmic processes in physiology, Nature, 410 (2001), 277-284.
doi: 10.1038/35065745. |
[11] |
B. Gutkin and B. Ermentrout, Dynamics of membrane excitability determine interspike interval variability: A link between spike generation mechanisms and cortical spike train statistics, Neural Comput., 10 (1998), 1047-1065.
doi: 10.1162/089976698300017331. |
[12] |
B. Gutkin, J. Jost and H. Tuckwell, Inhibition of rhythmic neural spiking by noise: The occurrence of a minimum in activity with increasing noise, Naturwiss., 96 (2009), 1091-1097.
doi: 10.1007/s00114-009-0570-5. |
[13] |
A. L. Hodgkin and A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol., 117 (1952), 500-544. |
[14] |
J. Honerkamp, G. Mutschler and R. Seitz, Coupling of a slow and a fast oscillator can generate bursting, Bull. Math. Biol., 47 (1985), 1-21.
doi: 10.1016/S0092-8240(85)90002-3. |
[15] |
G. Katriel, Synchronization of oscillators coupled through an environment, Physica D, 237 (2008), 2933-2944.
doi: 10.1016/j.physd.2008.04.015. |
[16] |
H. Kori, Y. Kawamura and N. Masuda, Structure of cell networks critically determines oscillation regularity, J. Theor. Biol., 297 (2012), 61-72.
doi: 10.1016/j.jtbi.2011.12.007. |
[17] |
Y. Kuramoto, "Chemical Oscillations, Waves, and Turbulence," Springer Series in Synergetics, 19, Springer-Verlag, Berlin, 1984.
doi: 10.1007/978-3-642-69689-3. |
[18] |
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.
doi: 10.1162/08997660360675035. |
[19] |
J. Nagumo, S. Arimoto and S. Yoshizawa, An active pulse transmission line simulating nerve axon, Proc. IRE, 50 (1962), 2061-2070.
doi: 10.1109/JRPROC.1962.288235. |
[20] |
A. Pikovsky, M. Rosenblum and J. Kurths, "Synchronization: A Universal Concept in Nonlinear Sciences," Cambridge Nonlinear Science Series, 12, Cambridge University Press, Cambridge, 2001.
doi: 10.1017/CBO9780511755743. |
[21] |
K. Sugimoto, Y. Nii, S. Doi and S. Kumagai, Frequency variability of neural rhythm in a small network of pacemaker neurons, Proc. of AROB 7th '02, (2002), 54-57. |
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