Nonlinear cooperative dynamics of living neurons

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 10, Issue 5, 2000, Pages 913-933

  Rabinovich, Mikhail I ^a   Varona, Pablo ^a   Abarbanel, Henry D I ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA SAN DIEGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMALIA;

EID: 0013369377     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127400000669     Document Type: Review

References (47)

1. Abarbanel, H. D. I., Huerta, R., Rabinovich, M. I., Rulkov, N. F., Rowat, P. & Selverston, A. I. [1996] "Synchronized action of synaptically coupled chaotic model neurons," Neural Comput. 8, 1567.
2. Afraimovich, V. S., Verichev, N. N. & Rabinovich, M. I. [1986] "Stochastic synchronization in dissipative systems," Izv. VUZ Radiofiz. RPQAEC 29, 795.
3. Bal, T., Nagy, F. & Moulins, M. [1998] "The pyloric central pattern generator in crustacea: A set of conditional neuronal oscillators," J. Comparative Physiol. A163, 715.
4. Berridge, M. J. [1998] "Neuronal calcium signaling," Neuron 21, 13.
5. Douglas, R. J. & Martin, K. C. [1991] "Opening the grey box," TINS 14(7), 286.
6. Elson, R., Selverston, A. I., Huerta, R., Rabinovich, M. I. & Abarbanel, H. D. I. [1998] "Synchronous behavior of two coupled biological neurons," Phys. Rev. Lett. 81(25), 5692.
7. Elson, R., Huerta, R., Abarbanel, H. D. I., Rabinovich, M. I. & Selverston, A. I. [1999] "Dynamical control of irregular bursting in an identified neuron of an oscillatory circuit," J. Neurophysiol. 82, 115.
8. 3," Biol. Cybern. 82, (May).
9. Getting, P. A. [1989] "Emerging principles governing the operation of neural networks," Ann. Rev. Neurosci. 12, 185.
10. Grillner, S., Wallén, P. & Brodin, L. [1991] "Neuronal network generating locomotor behavior in lamprey: Circuitry, transmitters, membrane properties, and simulation," Ann. Rev. Neurosci. 14, 169.
11. Heagy, J. F., Pecora, L. M. & Carrol, T. L. [1994] "Synchronuous chaos in coupled oscillator systems," Phys. Rev. E50, 1874.
12. Hindmarsh, J. L. & Rose, R. M. [1984] "A model of neuronal bursting using three first order differential equations," Proc. R. Soc. Lond. B221, 87.
13. Hodgkin, A. L. & Huxley, A. F. [1952] "A quantitative description of membrane current and its application to conduction and excitation in nerve," J. Physiol. 117, 500.
14. Huerta, R., Rabinovich, M. I., Abarbanel, H. D. I. & Bazhenov, M. [1997] "Spike-train bifurcation scaling in two coupled chaotic neurous," Phys. Rev. E55, R2108.
15. Huerta, R., Bazhenov, M. & Rabinovich, M. [1998] "Clasters of synchronization and bistability in lattices of chaotic neurons," Europhys. Lett. 43, 719.
16. Koch, C. & Segev, I. [1998] Methods in Neuronal Modeling (MIT Press).
17. Kristan, W. B. [1980] "Generation of rhythmic motor patterns," Information Processing in the Nervous System (Raven Press, NY).
18. Laurent, G., Wehr, M. & Davidowitz, H. [1996] "Temporal representation of odors in an olfactory network," The J. Neurosci. 16(2), 3837.
19. 2+ oscillations," Am. J. Physiol 269(5 Pt 1), C1079.
20. Li, Y.-X., Rinzel, J. & Stojilkovic, S. S. [1995] "Spontaneous electrical and calcium oscillations in unstimulated pituitary gonadotrophs," Biophys. J. 69, 785.
21. Li, Y.-X., Stojilkovic, S. S., Keizer, J. & Rinzel, J. [1997] "Sensing and refilling calcium stores in a excitable cell," Biophys. J. 72, 1080.
22. Llinás, R., Lang, E. J. & Welsh, J. P. [1997] "The cerebellum, LTD, and memory: Alternative views," Learning & Memory 3, 445.
23. Llinás, R. & Welsh, J. P. [1993] "On the cerebellum and motor learning," Curr. Opin. Neurobiol. 3, 958.
24. Mori, K. & Shepherd, G. M. [1994] "Emerging principles of molecular signal processing by mitral/tufted cells in the olfactory bulb," Seminars in Cell Biol. 5(1), 65.
25. 3) receptor in mouse cerebellar purkinje cells using three monoclonal antibodies," Cell Structure and Function 15, 163.
26. Parker, T. S. & Chua, L. O. [1989] Practical Numerical Algorithms for Chaotic Systems (Springer, NY).
27. Pearce, T. C. [1997] "Computational parallels between the biological olfactory pathway and its analogue 'the electronic nose'," Biosyst. 41(1), 43.
28. Pecora, L. M. & Carroll, T. L. [1990] "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821.
29. Prechtl, J. C., Cohen, L. B., Pesaran, B., Mitra, P. P. & Kleinfeld, D. [1997] "Visual stimuli induce waves of electrical activity in turtle cortex," Proc. Natl. Acad. Sci. USA 94, 7621.
30. Rabinovich, M. I., Huerta, R., Bazhenov, M., Kozlov, A. K. & Abarbanel, H. D. I. [1998a] "Computer simulations of stimulus dependent state switching in basic circuits of bursting neurons," Phys. Rev. E58, 6418.
31. Rabinovich, M., Bazhenov, M., Huerta, R., Abarbanel, H. D. I. & Laurent, G. [1998b] "A model of transient synchronization in locust antennal lobe circuits," Soc. Neurosci. Abst. 24, 359.6.
32. Rabinovich, M. I. & Abarbanel, H. D. I. [1998c] "The role of chaos in neural systems," Neurosci. 87(1), 5.
33. Rabinovich, M. I., Varona, P., Torres, J. J., Huerta, R. & Abarbanel, H. D. I. [1999a] "Slow dynamics and regularization phenomena in ensembles of chaotic neurons," Physica A263, 405.
34. Rabinovich, M., Huerta, R., Volkovskii, A., Abarbanel, H. D. I. & Laurent, G. [1999b] "Sensory coding with dynamically competitive networks," available at http://arXiv.org/abs/neuro-sys/9905002v2.
35. Rabinovich, M., Torres, J. J., Varona, P., Huerta, R. & Weidman, R. [1999c] "Origin of coherent structures in a discrete chaotic medium," Phys. Rev. E60, R1130.
36. Richardson, K. A., Imhoff, T. T., Grigg, P. & Collins, J. J. [1998] "Encoding chaos in neural spike trains," Phys. Rev. Lett. 80(11), 2485.
37. Rolls, E. T. & Treves, A. [1998] Neural Networks and Brain Function (Oxford University Press).
38. Rulkov, N. F. & Volkovskii, A. R. [1993] "Threshold synshronization of chaotic relaxation oscillators," Phys. Lett. A179, 332.
39. Satoh, T., Ross, Ch. A., Villa, A., Supattapone, S., Pozzan, T., Snyder, S. H. & Meldolesi, J. [1990] "The inositol 1, 4, 5-trisphosphate receptor in cerebellar purkinje cells: Quantitative immunogold labeling reveals concentration in an ER subcompartment," The J. Cell Biol. 111, 615.
40. Selverston, A. I. & Moulins, M. [1987] The Crustacean Stomatogastric System (Springer-Verlag, Berlin).
41. Selverston, A. I., Pachin, Y. V., Arshavsky, Y. I. & Orlovsky, G. N. [1997] "Shared features of invertebrate central pattern generators," Neurons, Networks and Motor Behavior (MIT Press).
42. Shevelev, I. A., Tsicalov, E. N., Gorbach, A. M., Budko, K. P. & Sharaev, G. A. [1993] "Thermoimaging of brain," J. Neurosci. Methods 46, 49.
43. Steriade, M., McCormick, D. A. & Sejnowski, T. J. [1993] "Thalamocortical oscillations in the sleeping and arousal brain," Science 262, 679.
44. Ullstrom, M., Kotaleski, J. H., Tegner, J., Aurell, E., Grillner, S. & Lansner, A. [1998] "Activity-dependent modulation of adaptation produces a constant burst proportion in a model of the lamprey spinal locomotor generator," Biol. Cybern. 79(1), 1.
45. Varona, P., Torres, J. J., Huerta, R., Rabinovich, M. I. & Abarbanel, H. D. I. [1999] "Regulation mechanisms in the bursting behavior of central pattern generator neurons: A modeling study," to be submitted to J. Neurophysiol.
46. Walton, P. D., Airey, J. A., Sutko, J. L., Beck, C. F., Mignery, G. A., Südhof, T. C., Deerinck, T. J. & Ellisman, M. H. [1991] "Ryanodine and inositol trisphosphate receptors coexist in avian cerebellar purkinje neurons," The J. Cell Biol. 113, 1145.
47. Wang, X.-J. [1993] Physica D6, 263.