Survival of subthreshold oscillations: The interplay of noise, bifurcation structure, and return mechanism

Discrete and Continuous Dynamical Systems - Series S

Volumn 2, Issue 4, 2009, Pages 873-895

  Kuske, Rachel ^a   Borowski, Peter ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Coherence resonance; Delay bifurcation; Integrate and fire; Mixed mode oscillations; Stochastic dynamics; Sub threshold oscillations

Indexed keywords

EID: 78650706645     PISSN: 19371632     EISSN: 19371179     Source Type: Journal    
DOI: 10.3934/dcdss.2009.2.873     Document Type: Article

References (34)

1. C. D. Acker, N. Kopell and J. A. White, Synchronization of strongly coupled excitatory neurons: relating network behavior to biophysics, J. Comp. Neuroscience, 15 (2003), 71-90. (Pubitemid 36992478)
2. A. Alonso and R. Klink, Differential electroresponsiveness of stellate and pyramidal-like cells of medial entorhinal cortex layer II, J. Neurophysiol., 70 (1993), 128-143. (Pubitemid 23220304)
3. S. M. Baer and E. M. Gaekel, Slow acceleration and deacceleration through a Hopf bifurcation: Power ramps, target nucleation, and elliptic bursting, Phys. Rev. E, 78 (2008), 036205.
4. S. M. Baer, T. Erneux and J. Rinzel, The slow passage through a Hopf bifurcation: Delay, memory effects, and resonance, SIAM J. Appl. Math., 49 (1989), 55-71.
5. N. Berglund and B. Gentz, Pathwise description of dynamic pitchfork bifurcations with additive noise, Probab. Theory Related Fields, 122 (2002), 341-388. (Pubitemid 36185842)
6. P. Borowski, J. L. Cabrera, R. Kuske and Y. X. Li, Influence of noise and bifurcation structure on subthreshold oscillations in mixed mode oscillations, in preparation.
7. J. C. Celet, D. Dangoisse, P. Glorieux, G. Lythe and T. Erneux, Slowly passing through resonance strongly depends on noise, Phys. Rev. Lett., 81 (1998), 975-978. (Pubitemid 128628889)
8. R. E. L. DeVille and C. S. Peskin, Synchrony and asynchrony in a fully stochastic neural network, Bull. Math. Biol., 70 (2008), 1608-1633.
9. h in the pacing of subthreshold oscillations in entorhinal cortex layer II neurons, J. Neurophysiol., 83 (2000), 2562-2579. (Pubitemid 30321451)
10. G. B. Ermentrout and C. C. Chow, Modeling neural oscillations, Physiology & Behavior, 77 (2002), 629-633. (Pubitemid 36084412)
11. E. Fransen, A. A. Alonso, C. T. Dickson, J. Magistretti and M. E. Hasselmo, Ionic mechanisms in the generation of subthreshold oscillations and action potential clustering in entorhinal layer II stellate neurons, Hippocampus, 14 (2004), 368-384. (Pubitemid 38594412)
12. M. Georgiou and T. Erneux, Pulsating laser oscillations depend on extremely-small-amplitude noise, Phys. Rev. A, 45 (1992), 6636-6642.
13. E. M. Izhikevich, Resonate and fire neurons, Neural Networks, 14 (2001), 883-894.
14. E. M. Izhikevich, Synchronization of elliptic bursters, SIAM Rev., 43 (2001), 315-344. (Pubitemid 32697798)
15. M. M. Klosek and R. Kuske, Multiscale analysis of stochastic delay differential equations, Multiscale Model. Simul., 3 (2005), 706-729. (Pubitemid 41269716)
16. M. Krupa and P. Szmolyan, Relaxation oscillation and canard explosion, J. Differential Equations, 174 (2001), 312-368. (Pubitemid 33378729)
17. M. Krupa and P. Szmolyan, Extending slow manifolds near trans-critical and pitchfork singularities, Nonlinearity, 14 (2001), 1473-1491. (Pubitemid 33401561)
18. R. Kuske, Probability densities for noisy delay bifurcations, J. Statist. Phys., 96 (1999), 797-816.
19. R. Kuske and S. Baer, Asymptotic analysis of noise sensitivity in a neuronal burster, Bull. Math. Biol., 64 (2002), 447-481. (Pubitemid 38370203)
20. R. Kuske and G. Papanicolaou, The invariant density of a chaotic dynamical system with small noise, Physica D, 120 (1998), 255-272. (Pubitemid 128676679)
21. G. D. Lythe and M. R. E. Proctor, Noise and slow-fast dynamics in a 3-wave resonance problem, Phys. Rev. E, 47 (1993), 3122-3127.
22. V. A. Makarov, V. I. Nekorkin and M. G. Velarde, Spiking Behavior in a Noise-Driven system combining oscillatory and excitatory properties, Phys. Rev. Lett., 86 (2001), 3431-3434. (Pubitemid 32380653)
23. C. B. Muratov and E. Vanden-Eijnden, Noise-induced mixed-mode oscillations in a relaxation oscillator near the onset of a limit cycle, Chaos, 18 (2008), 015111.
24. A. S. Pikovsky and J. Kurths, Coherence resonance in a noise-driven excitable system, Phys. Rev. Lett., 78 (1997), 775-778. (Pubitemid 127648034)
25. S. Reinker, Y. X. Li and R. Kuske, Noise-induced coherence and network oscillations in a reduced bursting model, Bull. Math. Biol., 68 (2006), 1401-1427. (Pubitemid 44174950)
26. H. G. Rotstein, T. Oppermann, J. A. White and N. Kopell, The dynamic structure underlying subthreshold oscillatory activity and the onset of spikes in a model of medial entorhinal cortex stellate cells, J. Comput. Neurosci., 21 (2006), 271-292. (Pubitemid 44524531)
27. H. G. Rotstein, M. Wechselberger and N. Kopell, Canard induced mixed-mode oscillations in a medial entorhinal cortex layer II stellate cell model, SIAM J. Appl. Dyn. Syst., 7 (2008), 1582-1611.
28. A. P. Sripati and K. O. Johnson, Dynamic gain changes during attentional modulation, Neural Computation, 18 (2006), 1847-1867. (Pubitemid 44036397)
29. J. Su, J. Rubin and D. Terman, Effects of noise on elliptic bursters, Nonlinearity, 17 (2004), 133-157. (Pubitemid 38085739)
30. M. Wechselberger and W. Weckesser, Bifurcations of mixed-mode oscillations in a stellate cell model, to appear in Physica D.
31. M. Wechselberger and W. Weckesser, Homoclinic clusters and chaos associated with a folded node in a stellate cell model, to appear in DCDS-S.
32. J. A. White, R. Klink, A. Alonso and A. R. A. Kay, Noise from voltage-gated ion channels may influence neuronal dynamics in the entorhinal cortex, preprint J. Neurophysiol., 80 (1998), 262-269. (Pubitemid 28326260)
33. H.-Y. Wu and S. M. Baer, Analysis of an excitable dendritic spine with an activity-dependent stem conductance, J. Math. Biol., 36 (1998), 569-592. (Pubitemid 128735364)
34. N. Yu, R. Kuske and Y. X. Li, Stochastic phase dynamics: multiscale behavior and coherence measures, Phys. Rev. E, 73 (2006), 056205.