Fokker-Planck analysis of stochastic coherence in models of an excitable neuron with noise in both fast and slow dynamics

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 72, Issue 3, 2005, Pages

  Hilborn, Robert C ^a   Erwin, Rebecca J ^b  

^a AMHERST COLLEGE   (United States)

^b California Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COHERENCE RESONANCE; FOKKER-PLANCK ANALYSIS;

ELEMENTARY PARTICLES; MATHEMATICAL MODELS; RANDOM PROCESSES; RESONANCE;

HIGH ENERGY PHYSICS;

EID: 28844433105     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.031112     Document Type: Article

References (58)

1. L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.70.223 70, 223 (1998).
2. Hu Gang, T. Ditzinger, C. Z. Ning, and H. Haken, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.807 71, 807 (1993).
3. A. Longtin, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.55.868 55, 868 (1997).
4. A. S. Pikovsky and J. Kurths, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.775 78, 775 (1997).
5. A. Zaikin and J. Kurths, Chaos CHAOEH 1054-1500 10.1063/1.1380369 11, 570 (2001).
6. S.-G. Lee, A. Neiman, and S. Kim, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.57.3292 57, 3292 (1998).
7. J. L. A. Dubbeldam, B. Krauskopf, and D. Lenstra, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.6580 60, 6580 (1999).
8. S. R. Massanes and C. J. Perez Vicente, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.59.4490 59, 4490 (1999).
9. B. Lindner and L. Schimansky-Geier, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.7270 60, 7270 (1999).
10. J. R. Pradines, G. V. Osipov, and J. J. Collins, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.6407 60, 6407 (1999).
11. V. A. Makarov, V. I. Nekorkin, and M. G. Velarde, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.3431 86, 3431 (2001).
12. B. Lindner and L. Schimansky-Geier, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.61.6103 61, 6103 (2000).
13. S. K. Han, T. G. Yim, D. E. Postnov, and O. V. Sosnovtseva, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.1771 83, 1771 (1999).
14. Y. Horikawa, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.031905 64, 031905 (2001).
15. Y. Shinohara, T. Kanamaru, H. Suzuki, T. Horita, and K. Aihara, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.051906 65, 051906 (2002).
16. E. I. Volkov, M. N. Stolyarov, A. A. Zaikin, and J. Kurths, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.066202 67, 066202 (2003).
17. C. Palenzuela, R. Toral, C. R. Mirasso, O. Calvo, and J. D. Gunton, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2001-00526-5 56, 347 (2001).
18. Z. Liu and Y.-C. Lai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.4737 86, 4737 (2001).
19. Y.-C. Lai and Z. Liu, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.066202 64, 066202 (2001).
20. A. Neiman, L. Schimansky-Geier, A. Cornell-Bell, and F. Moss, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.4896 83, 4896 (1999).
21. C. Zhou, J. Kurths, and B. Hu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.098101 87, 098101 (2001).
22. C. Masoller, Physica D PDNPDT 0167-2789 168, 171 (2002).
23. L. I and J.-M. Liu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.3161 74, 3161 (1995).
24. D. E. Postnov, S. K. Han, T. G. Yim, and O. V. Sosnovtseva, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.59.R3791 59, R3791 (1999).
25. G. Giacomelli, M. Giudici, S. Balle, and J. R. Tredicce, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.3298 84, 3298 (2000).
26. A. G. Balanov, N. B. Janson, D. E. Postnov, and P. V. E. McClintock, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.041105 65, 041105 (2002).
27. K. Miyakawa and H. Isikawa, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.046204 66, 046204 (2002).
28. I. Z. Kiss, J. L. Hudson, G. J. Escalera Santos, and P. Parmananda, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.035201 67, 035201 (R) (2003).
29. C. S. Zhou, J. Kurths, E. Allaria, S. Boccaletti, R. Meucci, and F. T. Arecchi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.066220 67, 066220 (2003).
30. B. Lindner, J. García-Ojalvo, A. Neiman, and L. Schimansky-Geier, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2003.10.015 392, 321 (2004).
31. R. C. Hilborn and R. J. Erwin, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2003.12.040 322, 19 (2004).
32. N. F. Rulkov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.183 86, 183 (2001).
33. C. Morris and H. Lecar, Biophys. J. BIOJAU 0006-3495 35, 193 (1981).
34. R. C. Hilborn (unpublished).
35. J. G. Nicholls, A. R. Martin, B. G. Wallace, and P. A. Fuchs, From Neuron to Brain (Sinauer Associates, Sunderland, MA, 2001).
36. N. F. Rulkov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.041922 65, 041922 (2002).
37. G. de Vries, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.051914 64, 051914 (2001).
38. R. C. Hilborn, Am. J. Phys. AJPIAS 0002-9505 10.1119/1.1645283 72, 528 (2004).
39. A. Alonso and R. R. Llinás, Nature (London) NATUAS 0028-0836 10.1038/342175a0 342, 175 (1989).
40. A. Alonso and R. Klink, J. Neurophysiol. JONEA4 0022-3077 70, 128 (1993).
41. B. Hu and C. Zhou, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.61.R1001 61, R1001 (2000).
42. P. Dayan and L. F. Abbott, Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems (MIT Press, Cambridge, 2001).
43. C. W. Gardiner, Handbook of Stochastic Methods (Springer, Berlin, 1985).
44. H. Risken, The Fokker-Planck Equation (Springer, Berlin, 1989).
45. W. Paul and J. Baschnagel, Stochastic Processes (Springer, Berlin, 1999).
46. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier, Amsterdam, 1992).
47. A. M. Lacasta, F. Sagues, and J. M. Sancho, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.045105 66, 045105 (R) (2002).
48. H. Haken, Synergetics, An Introduction (Springer-Verlag, Berlin, 1983).
49. S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, Reading, MA, 1994).
50. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: The Art of Scientific Computing (Cambridge University Press, Cambridge, England, 2002).
51. R. C. Hilborn, Chaos and Nonlinear Dynamics (Oxford University Press, Oxford, 2000).
52. D. Gillespie, Markov Processes (Academic Press, Boston, 1992).
53. D. S. Lemons, An Introduction to Stochastic Processes in Physics (Johns Hopkins University Press, Baltimore, 2002).
54. R. FitzHugh, Biophys. J. BIOJAU 0006-3495 1, 445 (1961).
55. J. Nagumo, S. Arimoto, and S. Yoshizawa, Proc. IRE PIREAE 0096-8390 50, 2061 (1962).
56. W. C. Stacey and D. M. Durand, J. Neurophysiol. JONEA4 0022-3077 86, 1104 (2001).
57. J.-W. Shuai and P. Jung, Biophys. J. BIOJAU 0006-3495 83, 87 (2002).
58. S. C. Tovey, J. Cell. Sci. JNCSAI 0021-9533 114, 3979 (2001).