Resonances and noise in a stochastic Hindmarsh-Rose model of thalamic neurons

Bulletin of Mathematical Biology

Volumn 65, Issue 4, 2003, Pages 641-663

  Reinker, Stefan ^a   Puil, Ernest ^a   Miura, Robert M ^a,b  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b NEW JERSEY INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038306355     PISSN: 00928240     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0092-8240(03)00026-0     Document Type: Article

References (44)

1. Arnold, L. (1998). Random Dynamical Systems, Berlin: Springer.
2. Baltanas, J. P. and J. M. Casado (2002). Noise-induced resonances in the Hindmarsh-Rose neuronal model. Phys. Rev. E 65, 041915.
3. Berdichevsky, V. and M. Gitterman (1996). Stochastic resonance in a bistable piecewise potential: analytical solution. J. Phys. A 29, L447-L452.
4. Braun, H. A., H. Wissing, K. Schäfer and M. C. Hirsch (1994). Oscillation and noise determine signal transduction in shark multimodal sensory cells. Nature 367, 270-273.
5. Chapeau-Blondeau, F., X. Godivier and N. Chambet (1996). Stochastic resonance in a neuron model that transmits spike trains. Phys. Rev. E 53, 1273-1275.
6. Destexhe, A., M. Neubig, D. Ulrich and J. Huguenard (1998). Dendritic low-threshold calcium currents in thalamic relay cells. J. Neurosci. 18, 3574-3588.
7. Douglass, J. K., L. Wilkens, E. Pantazelou and F. Moss (1993). Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance. Nature 365, 337-340.
8. FitzHugh, R. (1961). Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1, 445-466.
9. Gammaitoni, L., P. Hänggi, P. Jung and F. Marchesoni (1998). Stochastic resonance. Rev. Mod. Phys. 70, 223-287.
10. Gardiner, C. W. (1983). Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, Berlin: Springer.
11. Godivier, X. and F. Chapeau-Blondeau (1996). Noise-enhanced transmission of spike trains in the neuron. Europhys. Lett. 35, 473-477.
12. Hänggi, P., P. Jung, C. Zerbe and F. Moss (1993). Can colored noise improve stochastic resonance? J. Stat. Phys. 70, 25-47.
13. Hindmarsh, J. L. and R. M. Rose (1984). A model of neuronal bursting using three coupled first order differential equations. Proc. R. Soc. Lond. B Biol. Sci. 221, 87-102.
14. Hutcheon, B., R. M. Miura and E. Puil (1996). Models of subthreshold membrane resonance in neocortical neurons. J. Neurophysiol. 76, 698-714.
15. Hutcheon, B., R. M. Miura, Y. Yarom and E. Puil (1994). Low-threshold calcium current and resonance in thalamic neurons: a model of frequency preference. J. Neurophysiol. 71, 583-594.
16. Hutcheon, B. and Y. Yarom (2000). Resonance, oscillation, and the intrinsic frequency preferences of neurons. TINS 23, 216-222.
17. Jansons, K. M. and G. D. Lythe (1998). Stochastic calculus application to dynamic bifurcations and threshold crossings. J. Stat. Phys. 90, 227-251.
18. Jaramillo, F. and K. Wiesenfeld (1998). Mechanoelectrical transduction assisted by brownian motion: a role for noise in the auditory system. Nat. Neurosci. 1, 384-388.
19. Kloeden, P. E. and E. Platen (1992). Numerical Solution of Stochastic Differential Equations, Berlin: Springer.
20. Lindner, B. and L. Schimansky-Geier (2000). Coherence and stochastic resonance in a two-state system. Phys. Rev. E 61, 6103-6110.
21. Longtin, A. (1993). Stochastic resonance in neuron models. J. Stat. Phys. 70, 309-327.
22. Longtin, A. (1997). Autonomous stochastic resonance in bursting neurons. Phys. Rev. E 55, 868-876.
23. Longtin, A., A. Bulsara and F. Moss (1991). Time-interval sequences in bistable systems and the noise-induced transmission of information by sensory neurons. Phys. Rev. Lett. 67, 656-659.
24. Longtin, A. and D. Chialvo (1998). Stochastic and deterministic resonances for excitable systems. Phys Rev. Lett. 81, 4012-4015.
25. Longtin, A. and K. Hinzer (1996). Encoding with bursting, subthreshold oscillations, and noise in mammalian cold receptors. Neural Comp. 8, 215-255.
26. Massanes, S. and C. Vicente (1999). Nonadiabatic resonances in a noisy FitzHugh-Nagumo neuron model. Phys. Rev. E 59, 4490-4497.
27. Meunier, C. and A. D. Verga (1988). Noise and bifurcations. J. Stat. Phys. 50, 345-375.
28. Morse, R. P. and E. F. Evans (1996). Enhancement of vowel coding for cochlear implants by addition of noise. Nat. Med. 2, 928-932.
29. Moss, F., D. Pierson and D. O' Gorman (1994). Stochastic resonance: tutorial and update. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 4, 1383-1397.
30. Nagao, N., H. Nishimura and N. Matsui (2000). A neural chaos model of multistable perception. Neural Processing Lett. 12, 267-276.
31. Nagumo, J. S., S. Arimoto and S. Yoshizawa (1962). An active pulse transmission line simulating nerve axon. Proc. IRE. 50, 2061-2071.
32. Osipov, V. V. and E. V. Ponizovskaya (2000). Multivalued stochastic resonance in a model of an excitable neuron. Phys. Lett. A 271, 191-197.
33. Press, W. H. (1992). Numerical Recipes in C: The Art of Scientific Computing, New York: Cambridge University Press.
34. Puil, E., H. Meiri and Y. Yarom (1994). Resonant behavior and frequency preference of thalamic neurons. J. Neurophysiol. 71, 575-582.
35. Robinson, J. W. C., D. E. Asraf, A. R. Bulsara and M. E. Inchiosa (1998). Information-theoretic distance measures and a generalization of stochastic resonance. Phys. Rev. Lett. 81, 2850-2853.
36. Shimokawa, T., K. Pakdaman and S. Sato (1999). Time-scale matching in the response of a leaky integrate-and-fire neuron model to periodic stimulus with additive noise. Phys. Rev. E 59, 3427-3443.
37. Stacey, W. C. and D. M. Durand (2000). Stochastic resonance improves signal detection in hippocampal CA1 neurons. J. Neurophysiol. 83, 1394-1402.
38. Tanabe, S. and K. Pakdaman (2001a). Dynamics of moments of FitzHugh-Nagumo neuronal models and stochastic bifurcations. Phys. Rev. E 63, 031911.
39. Tanabe, S. and K. Pakdaman (2001b). Noise-enhanced neuronal reliability. Phys. Rev. E 64, 041904.
40. Terman, D. (1991). Chaotic spikes arising from a model of bursting in excitable membranes. SIAM J. Appl. Math. 51, 1418-1450.
41. Terman, D. (1992). The transition from bursting to continuous spiking in excitable membrane models. J. Nonlinear Sci. 2, 135-182.
42. Tuckwell, H. C. (1989). Stochastic Processes in the Neurosciences, CBMS-NSF Regional Conference Series in Applied Mathematics 56, Philadelphia, PA: SIAM.
43. Wang, W., Y. Wang and Z. D. Wang (1998). Firing and signal transduction associated with an intrinsic oscillation in neuronal systems. Phys. Rev. E 57, R2527-R2530.
44. Wu, S., W. Ren, H. Kaifen and Z. Huang (2001). Burst and coherence resonance in Rose-Hindmarsh model induced by additive noise. Phys. Lett. A 279, 347-354.