Stochastic excitation and synchronization in coupled FitzHugh-Nagumo elements

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 5114, Issue , 2003, Pages 301-308

  Luchinsky, D G ^a   McClintock, P V E ^a   Polovinkin, A V ^b   Osipov, G V ^b  

^a LANCASTER UNIVERSITY   (United Kingdom)

^b LOBACHEVSKY STATE UNIVERSITY OF NIZHNY NOVGOROD   (Russian Federation)

Author keywords

FitzHugh Nagumo system; Fokker Planck equation; Optimal path; Stochastic activation

Indexed keywords

COMPUTER SIMULATION; HAMILTONIANS; MONTE CARLO METHODS; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES;

FITZHUGH-NAGUMO SYSTEM; FOKKER-PLANCK EQUATION; STOCHASTIC ACTIVATION;

SYNCHRONIZATION;

EID: 0042263276     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.489027     Document Type: Conference Paper

References (25)

1. R. J. White, J.A. and A. Kay, "Channel noise in neurons," Trends Neurosci. 23(3), pp. 131-137, 2000.
2. R. Benzi, A. Sutera, and A. Vulpiani, "The mechanism of stochastic resonance," J. of Phys. A 14(11), pp. L453-L457, 1981.
3. M. I. Dykman, R. Luchinsky, D. G. Mannela, P. V. E. McClintock, N. D. Stein, and N. Stocks, "Stochastic resonance in perspective," Nuovo Cimento D 17(7-8), pp. 661-683, 1995.
4. L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, "Stochastic resonance," Rev. Mod. Phys. 70(1), 223-287, 1998.
5. A. Pikovsky and J. Kurths, "Coherence resonance in a noise-driven excitable system," Phys. Rev. Lett 78(5), pp. 775-778, 1997.
6. C. Zhou, J. Kurths, and B. Hu, "Array-enhanced coherence resonance: nontrivial effets of heterogeneity annd spatial independence of noise," Phys. Rev. Lett 87(9), pp. 0981011-0981014, 2001.
7. J. Pradines, G. Osipov, and J. Collins, "Coherence resonance in excitable and oscillatory systems: The essential role of slow and fast dynamics," Phys. Rev. E 60(6), pp. 6407-6410, 1999.
8. w.-J. Rappel and A. Karma, "Noise-induced coherence resonance in neural networks," Phys. Rev. Lett 77(15), pp. 3256-3259, 1996.
9. S. Massanas and C. Perez Vicente, "Nonadiabatic resonances in a noisy fitzhugh-nagumo model," Phys. Rev. E 59(4), pp. 4490-4497, 1999.
10. P. Jung and G. Mayer-Kress, "Spatiotemporal stochastic resonance in excitable media," Phys. Rev. Lett 76(11), pp. 2130-2133, 1995.
11. C. Kurrer and K. Schulten, "Noise-induced synchronous neuronal oscillations," Phys. Rev. E 51(6), pp. 6213-6218, 1995.
12. B. Shulgin, A. Neiman, and V. Anishchenko, "Mean switching frequency locking in stochastic bistable systems driven by a periodic force," Phys. Rev. Lett 75(23), pp. 4157-4160, 1995.
13. B. Hu and C. Zhou, "Synchronization regimes in coupled noisy excitable systems," Phys. Rev. E 63(2), pp. 0262011-0262016, 2001.
14. J. F. Lindner, B. K. Meadows, W. L. Ditto, M. E. Inchiosa, and A. R. Bulsara, "Scaling laws for spatiotemporal synchronization and array enhanced stochastic resonance," Phys. Rev. E 53(3), pp. 2018-2086, 1996.
15. M. Santos and J. Sancho, "Noise-induced fronts," Phys. Rev. E 59(1), pp. 98-102, 1999.
16. H. Risken, The Fokker-Plank Equation, Springer, Berlin, 3 ed., 1996.
17. D. Ludwig, "Persistence of dynamical systems under random perturbations," SIAM Rev. 17(4), pp. 605-640, 1975.
18. M. Freidlin and A. D. Wentzel, Random Perturbations in Dynamical Systems, Springer, New-York, 1984.
19. R. Graham and T. Tel, "Existence of a potential for dissipative dynamical systems," Phys. Rev. Lett. 52, pp. 9-12, 1984.
20. R. Graham, Macroscopic potentials, bifurcation and noise in dissipative systems, vol. 1, Cambridge University Press, Cambridge, 1989.
21. M. I. Dykman, "Large fluctuations and fluctuational transitions in systems driven by colored gaussian noise-a high frequency noise," Phys. Rev. A 42, pp. 2020-2029, 1990.
22. R. S. Maier and D. L. Stein, "A scaling theory of bifurcations in the symmetrical weak-noise escape problem," J. Stat. Phys. 83, pp. 291-357, 1996.
23. R. S. Maier and D. L. Stein, "Limiting exit location distributions in the stochastic exit problem," SIAM J. Appl. Math. 57(3), pp. 752-790, 1997.
24. C. W. Gardiner, Handbook of stochastic methods, Springer, Berlin, 2 ed., 1990.
25. R. Graham and T. Tel, "Weak-noise limit of fokker-plank models and nondifferentiable potentials for dissipative dynamical systems," Phys. Rev. A 31(2), pp. 1109-1122, 1985.