Oscillatory response in a sensory network of on and off cells with instantaneous and delayed recurrent connections

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 368, Issue 1911, 2010, Pages 455-467

  Lefebvre, J ^a   Longtin, A ^a   Leblanc, V G ^a  

^a UNIVERSITY OF OTTAWA   (Canada)

Author keywords

Delayed feedback; Neural field; ON and OFF cells; Oscillations; Sensory inputs

Indexed keywords

HOPF BIFURCATION; NEURAL NETWORKS;

ANDRONOV-HOPF BIFURCATION; DELAYED FEEDBACK; FEEDBACK CONNECTION; INVERTED POLARITY; MULTIPLE CELLS; NEURAL FIELD; NEURAL FIELD MODELS; NEURAL FIELDS; OSCILLATORY RESPONSE; SENSORY INPUT; SENSORY NETWORKS;

FREQUENCY RESPONSE;

ANIMAL; ARTICLE; ARTIFICIAL NEURAL NETWORK; BIOLOGICAL MODEL; ELECTRIC FISH; NERVE CELL NETWORK; OSCILLOMETRY; PHYSIOLOGY; SENSORY FEEDBACK; SYSTEMS BIOLOGY; TIME;

ANIMALS; ELECTRIC FISH; FEEDBACK, SENSORY; MODELS, NEUROLOGICAL; NERVE NET; NEURAL NETWORKS (COMPUTER); OSCILLOMETRY; SYSTEMS BIOLOGY; TIME FACTORS;

EID: 76149107888     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2009.0229     Document Type: Article

References (31)

1. Berman, N. J. & Maler, L. 1999 Neural architecture of the electrosensory lateral line lobe: adaptations for coincidence detection, a sensory searchlight and frequency-dependent adaptive filtering. J. Exp. Biol. 202, 1243.
2. Blomquist, P., Wyller, J. & Einevoll, G. T. 2005 Localized activity patterns in two-population neuronal networks. Physica D 206, 180-212. (doi:10.1016/j.physd.2005.05.004) (Pubitemid 40822880)
3. Borgers, C., Epstein, S. & Kopell, N. J. 2008 Gamma oscillations mediate stimulus competition and attentional selection in a cortical network mode. Proc. Natl Acad. Sci. USA 421, 18 023-18 028. (doi:10.1073/pnas. 0809511105)
4. Bressloff, P. C., Folias, S. E., Prat, A. & Li, Y.-X. 2003 Oscillatory waves in inhomogeneous neural media. Phys. Rev. Lett. 91, 178101. (doi:10.1103/PhysRevLett.91.178101)
5. Campbell, S.-A., Bélair, J., Ohira, T. & Milton, J. 1995 Limit cycles, tori and complex dynamics in a second-order differential equation with delayed negative feedback. J. Dyn. Diff. Eq. 7, 213-236. (doi:10.1007/ BF02218819)
6. Chacron, M. J., Doiron, B., Maler, L., Longtin, A. & Bastian, J. 2003 Non-classical receptive field mediated biological switch in a sensory neuron's frequency tuning. Nature 423, 77-81. (doi:10.1038/nature01590) (Pubitemid 36569585)
7. Coombes, S. & Owen, M. R. 2004 Evans functions for integral neural field equations with Heaviside firing rate function. SIAM J. Appl. Dyna. Syst. 34, 574-600. (doi:10.1137/040605953) (Pubitemid 40578317)
8. Coombes, S. & Owen, M. R. 2005 Bumps, breathers, and waves in a neural network with spike frequency adaptation. Phys. Rev. Lett. 94, 148102. (doi:10.1103/PhysRevLett.94.148102)
9. Dhamala, M., Jirsa, V. K. & Ding, M. 2004 Enhancement of neural synchrony by time delay. Phys. Rev. Lett. 92, 074104. (doi:10.1103/PhysRevLett. 92.074104)
10. Doiron, B., Lindner, B., Longtin, A., Maler, L. & Bastian, J. 2004 Oscillatory activity in electrosensory neurons increases with the spatial correlation of the stochastic input stimulus. Phys. Rev. Lett. 93, 048101. (doi:10.1103/PhysRevLett.93.048101)
11. Engel, A. K., König, P., Kreiter, A. K., Schillen, T. B. & Singer W. 1992 Temporal coding in the visual cortex: new vistas on integration in the nervous system. Trends Neurosci. 15, 218-226. (doi:10.1016/0166-2236(92) 90039-B)
12. Fields, H. L., Malick, A. & Burnstein, R. 1995 Dorsal horn projection targets of ON and OFF cells in the rostral ventromedial medulla. J. Neurophys. 74, 1742-1759.
13. Folias, S. E. & Bressloff, P. 2005 Stimulus-locked waves and breathers in an excitatory neural network. SIAM J. Appl. Math. 65, 2067-2092. (doi:10.1137/040615171)
14. Galazyuk, A. V. & Feng, A. S. 2001 Oscillation may play a role in time domain central auditory processing. J. Neurosci. 21, RC147:1-5.
15. Golomb, D. & Ermentrout, G. B. 2001 Bistability in pulse propagation in networks of excitatory and inhibitory populations. Phys. Rev. Lett. 86, 4179. (doi:10.1103/PhysRevLett.86.4179) (Pubitemid 32443960)
16. Gray, C. M. & Singer, W. 1989 Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. Proc. Natl Acad. Sci. USA 86, 1698-1702. (doi:10.1073/pnas.86.5.1698) (Pubitemid 19078968)
17. Hahnloser, R., Douglas, R. J., Mahowald, M. & Hepp, K. 1999 Feedback interactions between neuronal pointers and maps for attentional processing. Nat. Neurosci. 2, 746-752. (doi:10.1038/11219) (Pubitemid 30491197)
18. Hutt, A. & Atay, F. M. 2005 Analysis of nonlocal neural fields for both general and gammadistributed connectivities. Physica D 203, 30-54. (doi:10.1016/j.physd.2005.03.002) (Pubitemid 40552574)
19. Hutt, A., Bestehorn, M. & Wennekers, T. 2003 Pattern formation in intracortical neuronal fields. Network: Comput. Neural Syst. 14, 351-368. (doi:10.1088/0954-898X/14/2/310) (Pubitemid 38002287)
20. Kandel, E. R. & Schwarz, J. H. 1983 Principles of neural science. New York, NY: Elsevier.
21. Laing, C. & Coombes, S. 2006 The importance of different timings of excitatory and inhibitory pathways in neural field models. Network 17, 151-172. (doi:10.1080/09548980500533461) (Pubitemid 44024989)
22. Laing, C. R. & Longtin, A. 2003 Dynamics of deterministic and stochastic paired excitatory- inhibitory delayed feedback. Neural Comput. 15, 2779-2822. (doi:10.1162/089976603322518740) (Pubitemid 37378995)
23. Lefebvre, J., Longtin, A. & LeBlanc, V. 2009 Dynamics of driven recurrent networks of ON and OFF cells. Phys. Rev. E 80, 041912. (doi:10.1103/PhysRevE.80.041912)
24. Lumer, D., Edelman, G. M. & Tononi, G. 1997 Neural dynamics in a model of the thalamocortical system. I. Layers, loops and the emergence of fast synchronous rhythms. Cerebral Cortex 7, 207-227. (doi:10.1093/cercor/7.3.207)
25. Marinazzo, D., Kappen, H. J. & Gielen, S. C. A. M. 2007 Input-driven oscillations in networks with excitatory and inhibitory neurons with dynamic synapses. Neural. Comp. 19, 1739-1765. (doi:10.1162/neco.2007.19.7.1739)
26. Meyer, U., Shao, J., Chakrabarty, S., Brandt, S. F., Luksch, H. &Wessel R. 2008 Distributed delays stabilize neural feedback systems. Biol. Cybernet. 99 79-87. (doi:10.1007/s00422-008-0239-8)
27. Pinto, D. & Ermentrout, G. B. 2001 Spatially structured activity in synaptically coupled neuronal networks I-II. SIAM J. Appl. Math. 62, 206-243. (doi:10.1137/S0036139900346453)
28. Robin, D. A. & Royer, R. L. 1987 Auditory temporal processing: two-tone flutter fusion and a model of temporal integration. J. Acoust. Soc. Am. 82, 1207. (doi:10.1121/1.395257)
29. Roxin, A., Brunel, N. & Hansel, D. 2005 The role of delays in shaping spatio-temporal dynamics of neuronal activity in large networks. Phys. Rev. Lett. 94, 238103. (doi:10.1103/PhysRevLett.94.238103)
30. Wang, D. L. 1999 Selection based on oscillatory correlation. Neural Netw. 12, 579-592. (doi:10.1016/S0893-6080(99)00028-3) (Pubitemid 29348430)
31. Wilson, H. R. & Cowan, J. D. 1972 Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12, 1-24. (doi:10.1016/S0006-3495(72)86068-5)