Noise induced synchronization in a neuronal oscillator

Physica D: Nonlinear Phenomena

Volumn 192, Issue 1-2, 2004, Pages 123-137

  Pakdaman, Khashayar ^a   Mestivier, Denis ^a  

^a INSERM   (France)

Author keywords

Lyapunov exponent; Neuron; Random dynamical system; Synchronization

Indexed keywords

ACOUSTICS; LYAPUNOV METHODS; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; SYNCHRONIZATION;

LYAPUNOV EXPONENTS; RANDOM DYNAMICAL SYSTEMS;

OSCILLATORS (MECHANICAL);

EID: 1842831264     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2003.12.006     Document Type: Article

References (39)

1. W.J. Adelman Jr., R. Fitzhugh, Solutions of the Hodgkin-Huxley equations modified for potassium accumulation in a periaxonal space, Fed. Proc. 34 (5) 1975.
2. Aihara K., Matsumoto G., Temporally coherent organization and instabilities in squid giant axons. J. Theoret. Biol. 95:1982;697-720.
3. Aihara K., Matsumoto G., Ikegaya Y., Periodic and non-periodic responses of a periodically forced Hodgkin-Huxley oscillator. J. Theoret. Biol. 109:1984;249-269.
4. L. Arnold, Random Dynamical Systems, Springer-Verlag, Berlin, 1998.
5. L. Arnold, G. Bleckert, K.R. Schenk-Hoppé, The stochastic brusselator: parametric noise destroys Hopf bifurcation, in: H. Crauel, M. Gundlach (Eds.), Stochastic Dynamics, Springer, New York, 1999, pp. 71-92.
6. L. Arnold, P. Imkeller, The kramers oscillator revisited, in: J. Freund, T. Pöschel (Eds.), Stochastic Processes in Physics, Chemistry, and Biology, vol. 557, Springer Lecture Notes in Physics, Springer, Berlin, 2000, pp. 280-291.
7. P. Bergé, Y. Pomeau, C. Vidal, Order within Chaos, Wiley, New York, 1986.
8. Bryant H., Segundo J.P., Spike initiation by transmembrane current: a white noise analysis. J. Physiol. 260:1976;279-314.
9. Crauel H., Flandoli F., Additive noise destroys a pitchfork bifurcation. J. Dyn. Diff. Eqns. 10(2):1998;259-274.
10. L. Glass, M.C. Mackey, From Clocks to Chaos, Princeton University Press, Princeton, 1988.
11. A. Goldbeter, Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behaviour, Cambridge University Press, Cambridge, 1996.
12. Guckenheimer J., Isochrons and phaseless sets. J. Math. Biol. 1:1975;259-273.
13. Hayashi H., Ishizuka S., Ohta M., Hirakawa K., Chaotic behavior in the onchidium giant neuron under sinusoidal forcing. Phys. Lett. A. 88:1982;435-438.
14. Hunter J.D., Milton J.G., Thomas P.J., Cowan J.D., Resonance effect for neural spike time reliability. J. Neurophysiol. 80:1998;1427-1438.
15. Kaplan D.T., Clay J.R., Manning T., Glass L., Guevara M.R., Shrier A., Subthreshold dynamics in periodically stimulated squid giant axons. Phys. Rev. Lett. 76(21):1996;4074-4077.
16. Kosmidis E.K., Pakdaman K., An analysis of the reliability phenomenon in the FitzHugh-Nagumo model. J. Comput. Neurosci. 14:2003;5-22.
17. E.K. Kosmidis, K. Pakdaman, Stochastic chaos in a neuronal model, Int. J. Bifurc. Chaos, in press.
18. Kroller J., Grusser O.J., Weiss L.R., Observations on phase-locking within the response of primary muscle spindle afferents to pseudo-random stretch. Biol. Cybernet. 59:1998;49-54.
19. Y. Kuramoto, Chemical Oscillations, Waves and Turbulence, Springer-Verlag, Berlin, 1984.
20. A. Lasota, M.C. Mackey, Chaos, Fractals and Noise: Stochastic Aspects of Dynamics, Springer-Verlag, Berlin, 1994.
21. Lestienne R., Spike timing, synchronization and information processing on the sensory side of the central nervous system. Prog. Neurobiol. 65:2001;545-591.
22. Lewis E.R., Henry K.R., Yamada W.M., Essential roles of noise in neural coding and in studies of neural coding. BioSystems. 58:2000;109-115.
23. Mainen Z.F., Sejnowski T.J., Reliability of spike timing in neocortical neurons. Science. 268:1995;1503-1506.
24. Pakdaman K., The reliability of the stochastic active rotator. Neural Comput. 14:2002;781-792.
25. Pakdaman K., Mestivier D., External noise synchronizes forced oscillators. Phys. Rev. E. 64:2001;030901(R).
26. Pakdaman K., Tanabe S., Random dynamics of the Hodgkin-Huxley neuron model. Phys. Rev. E. 64:2001;050902(R).
27. Pakdaman K., Tanabe S., Shimokawa T., Coherence resonance and discharge time reliability in neurons and neuronal models. Neural Netw. 14:2001;895-905.
28. Pham J., Pakdaman K., Champagnat J., Vibert J.-F., Activity in sparsely connected excitatory neural networks: effect of connectivity. Neural Netw. 11:1998;415-434.
29. Pham J., Pakdaman K., Vibert J.-F., A discrete map for the dynamics of recurrent excitatory neural networks in the presence of noise. BioSystems. 48:1998;179-186.
30. Pham J., Pakdaman K., Vibert J.-F., Noise-induced coherent oscillations in randomly connected neural networks. Phys. Rev. E. 58:1998;3623-3627.
31. Kara P., Reinagel P., Reid R.C., Low response variability in simultaneously recorded retinal, thalamic, and cortical neurons. Neuron. 27(3):2000;635-646.
32. Stiber M., Pakdaman K., Vibert J.F., Boussard E., Segundo J.P., Nomura T., Sato S., Doi S., Complex response of living neurons to pacemaker inhibition: a comparison of dynamical models. BioSystems. 40:1997;177-188.
33. Takahashi N., Hanyu Y., Musha T., Kubo R., Matsumoto G., Global bifurcation structure in periodically stimulated giant axons of squid. Physica D. 43:1990;318-334.
34. Takahata T., Tanabe S., Pakdaman K., White noise stimulation of the Hodgkin-Huxley model. Biol. Cybernet. 86:2002;403-417.
35. Tanabe S., Pakdaman K., Noise induced transition in neuronal models. Biol. Cybernet. 85(4):2001;269-280.
36. V. Wihstutz, Perturbation methods for Lyapunov exponent, in: H. Crauel, M. Gundlach (Eds.), Stochastic Dynamics, Springer, New York, 1999, pp. 209-239.
37. A.T. Winfree, The Geometry of Biological Time, vol. 8, Biomathematics, Springer-Verlag, Heidelberg, 1980.
38. Yamanobe T., Pakdaman K., Response of a pacemaker neuron model to stochastic pulse trains. Biol. Cybernet. 86:2002;155-166.
39. Yoshino K., Nomura T., Pakdaman K., Sato S., Synthetic analysis of periodically stimulated excitable and oscillatory membrane models. Phys. Rev. E. 59:1999;956-969.