Synchronized Action of Synaptically Coupled Chaotic Model Neurons

Neural Computation

Volumn 8, Issue 8, 1996, Pages 1567-1602

  Abarbanel, Henry D I ^a,b   Huerta, R ^b   Rabinovich, M I ^b   Rulkov, N F ^b   Rowat, P F ^b   Selverston, A I ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACTION POTENTIAL; ANIMAL; ARTICLE; BIOLOGICAL MODEL; CELL MEMBRANE POTENTIAL; CORTICAL SYNCHRONIZATION; ELECTROCHEMISTRY; NEPHROPIDAE; NERVE CELL; NERVE CELL INHIBITION; NONLINEAR SYSTEM; PHYSIOLOGY; STATISTICAL MODEL; SYNAPSE;

ACTION POTENTIALS; ANIMALS; CORTICAL SYNCHRONIZATION; ELECTROCHEMISTRY; MEMBRANE POTENTIALS; MODELS, NEUROLOGICAL; MODELS, STATISTICAL; NEPHROPIDAE; NEURAL INHIBITION; NEURONS; NONLINEAR DYNAMICS; SYNAPSES;

EID: 0030588574     PISSN: 08997667     EISSN: None     Source Type: Journal    
DOI: 10.1162/neco.1996.8.8.1567     Document Type: Article

References (28)

1. Abarbanel, H. D. I. 1995. Analysis of Observed Chaotic Data. Springer-Verlag, New York.
2. Abarbanel, H. D. I., Brown, R., Sidorowich, J. J., and Tsimring, L. 1993. The analysis of observed chaotic data in physical systems. Reviews of Modern Physics 65, 1331-1392.
3. Abarbanel, H. D. I., and Kennel, M. B. 1993. Local false nearest neighbors and dynamical dimensions from observed chaotic data. Phys. Rev. E 47, 3057-3068.
4. Adams, W. B., and Benson, J. 1985. The generation and modulation of endogenous rhythmicity in the Aplysia bursting pacemaker neuron R15. Prog. Biophys. Mol. Biol. 46, 1-49.
5. Afraimovich, V. S., Verichev, N. N., and Rabinovich, M. I. 1986. General synchronization. Izv. VUZ. Radiophiz. 29, 795-803.
6. Aihara, K., and Matsumoto, G. 1986. Chaotic oscillations and bifurcations in squid giant axons. In Chaos, pp. 257-269. Manchester University Press, Manchester.
7. Fraser, A. M., and Swinney, H. L. 1986. Independent coordinates for strange attractors. Phys. Rev. 33A, 1134.
8. Fujisaka, H., and Yamada, T. 1983. Stability theory of synchronized motion in coupled-oscillator systems. Prog. Theor. Phys. 69, 32-47.
9. Gallager, R. G. 1968. Information Theory and Reliable Communication. John Wiley, New York.
10. Guckenheimer, J., and Holmes, P. 1983. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer Verlag, New York.
11. Han, S. K., Kurrer, C., and Kuramoto, Y. 1995. Dephasing and bursting in coupled neural oscillators. Phys. Rev. Lett. 75, 3190.
12. Hayashi, H., and Ishizuka, S. 1992. Chaotic nature of bursting discharges in the Onchidium pacemaker neuron. J. Theor. Biol. 156, 269-291.
13. Hindmarsh, J. L., and Rose, R. M. 1984. A model of neuronal bursting using three coupled first order differential equations. Proc. R. Soc. Lond. B 221, 87-102.
14. Heagy, J. F., Carroll, T. L., and Pecora, L. M. 1994. Experimental and numerical evidence for riddled basins in coupled chaotic systems. Phys. Rev. Lett. 73, 3528-3531.
15. Hodgkin, A. L., and Huxley, A. F. 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. (London) 107, 500-544.
16. Kennel, M. B., Brown, R., and Abarbanel, H. D. I. 1992. Determining minimum embedding dimension using a geometrical construction. Phys. Rev. A 45, 3403-3411.
17. Mpitsos, George J., Burton, R. M., Creech, H. C., and Soinla, S. S. 1988. Evidence for chaos in spike trains of neurons that generate rhythmic motor patterns. Brain Res. Bull. 21, 529-538.
18. Oseledec, V. I. 1968. A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems. Trudy Mosk. Mat. Obsc. 19, 197.
19. Rabinovich, M. I., Huerta, R., Abarbanel, H. D. I., and Selverston, A. I. 1996. A minimal model for chaotic bursting of the LP neuron in lobster. Submitted to Proc. Natl. Acad. Sci.
20. Rinzel, J., and Ermentrout, G. B. 1989. Analysis of neural excitability and oscillations. In Methods in Neuronal Modeling, C. Koch and I. Segev, eds., pp. 135-160. MIT Press, Cambridge, MA.
21. Rose, R. M., and Hindmarsh, J. L. 1985. A model of thalmic neuron. Proc. Roy. Soc. Lond. B 225, 161-193.
22. Rulkov, N. F., Volkovskii, A. R., Rodriguez-Lozano, A., Del Rio, E., and Velarde, M. G. 1992. Mutual synchronization of chaotic self-oscillators with dissipative coupling. Int. J. Bif. Chaos 2, 669-676.
23. Selverston, A. I. 1996. Experiments on neurons within the STG Central Pattern Generator. Unpublished.
24. Sherman, A. 1994. Anti-phase asymmetric aperiodic oscillations in excitable cells - I. Coupled bursters. Bull Math. Biol. 56, 811-834.
25. Sherman, A., and Rinzel, J. 1992. Rhythmogenic effects of weak electrotonic coupling in neuronal models. Proc. Natl. Sci. U.S.A. 89, 2471.
26. Skinner, F. K., Kopell, N., and Marder, E. 1994. Mechanisms for oscillation and frequency control in reciprocally inhibitory model neural networks. J. Comp. Neuro. 1, 69.
27. Takens, F. 1981. In Dynamical Systems and Turbulence, Warwick 1980. Lecture Notes in Mathematics 898, D. Rand and L. S. Young, eds., p. 366. Springer, Berlin.
28. Vreeswijk C., Abbott, L. F. and Ermentrout G. B. 1994. When inhibition not excitation synchronizes neural firing. J. Compu. Neuro. 1, 313-321.