Synchronous behavior of two coupled electronic neurons

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 62, Issue 2, 2000, Pages 2644-2656

  Pinto, R D ^a   Varona, P ^a,b   Volkovskii, A R ^a   Szucs A ^a   Abarbanel, Henry D I ^a,c   Rabinovich, M I ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIOLOGICAL MATERIALS; COMPUTER SIMULATION; DEGREES OF FREEDOM (MECHANICS); DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; NEUROLOGY; SYNCHRONIZATION;

ELECTRONIC NEURONS; NONLINEAR OSCILLATORS; PANULIRUS INTERRUPTUS; STOMATOGASTRIC GANGLION; SYNAPTIC REVERSAL POTENTIALS;

NEURAL NETWORKS;

ANIMAL; BIOLOGICAL MODEL; BIOLOGICAL RHYTHM; COMPUTER SIMULATION; CYTOLOGY; ELECTROPHYSIOLOGY; GANGLION; MEMBRANE POTENTIAL; NEPHROPIDAE; NERVE CELL; PHYSIOLOGY; SYNAPSE;

ANIMALS; BIOLOGICAL CLOCKS; COMPUTER SIMULATION; ELECTROPHYSIOLOGY; GANGLIA, INVERTEBRATE; MEMBRANE POTENTIALS; MODELS, NEUROLOGICAL; NEPHROPIDAE; NEURONS; SYNAPSES;

EID: 0034238013     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.62.2644     Document Type: Article

References (31)

1. L. Glass and M. C. Mackey, From Clocks to Chaos: the Rhythms of Life (Princeton University Press, Princeton, NJ, 1988).
2. H. D. I. Abarbanel, R. Huerta, M. I. Rabinovich, P. F. Rowat, N. F. Rulkov, and A. I. Selverston, Neural Comput. 8, 1567 (1996).
3. H. D. I. Abarbanel, M. B. Kennel, M. Buhl, and C. Lewis, Phys. Rev. A 60, 2360 (1999).
4. R. Roy and G. VanWiggeren, Science 279, 1198 (1998).
5. M. I. Rabinovich and H. D. I. Abarbanel, Neuroscience 87, 5 (1998).
6. R. Elson, R. Huerta, N. F. Rulkov, H. D. I. Abarbanel, and M. I. Rabinovich, Phys. Rev. Lett. 81, 5692 (1998).
7. A. L. Hodgkin and A. F. Huxley, J. Physiol. (London) 117, 500 (1952).
8. M. Falcke, R. Huerta, M. I. Rabinovich, H. D. I. Abarbanel, R. C. Elson, and A. I. Selverston, Biol. Cybern. 82, 517 (2000).
9. M. I. Rabinovich, P. Varona, J. J. Torres, R. Huerta, and H. D. I. Abarbanel, Physica A 263, 405 (1999).
10. P. Varona, J. J. Torres, H. D. I. Abarbanel, M. I. Rabinovich, and R. E. Elson (unpublished).
11. H. D. I. Abarbanel, Analysis of Observed Chaotic Data (Springer, New York, 1996).
12. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, Cambridge, England, 1997).
13. J. L. Hindmarsh and R. M. Rose, Proc. R. Soc. London, Ser. B 221, 87 (1984).
14. A. Szücs, P. Varona, A. R. Volkovski, H. D. I. Abarbanel, M. I. Rabinovich, and A. I. Selverston, NeuroReport 11, 563 (2000).
15. T. S. Parker and L. O. Chua. Practical Numerical Algorithms for Chaotic Systems (Springer, New York, 1989).
16. Gordon M. Shepherd, Neurobiology, 3rd ed. (Oxford University Press, New York, 1994), see Chap. 7 for a discussion of these synaptic types.
17. A. A. Sharp, L. F. Abbott, and E. Marder, J. Neurophysiol. 67, 1691 (1992).
18. R. D. Pinto, A. Szücs, R. Elson, M. I. Rabinovich, and H. D. I. Abarbanel (unpublished).
19. V. S. Afraimovich, N. N. Verichev, and M. I. Rabinovich, Radiophys. Quantum Electron. 29, 747 (1986).
20. J. F. Heagy, L. M. Pecora, and T. L. Carroll, Phys. Rev. E 50, 1874 (1994).
21. N. F. Rulkov, A. R. Volkovskii, A. Rodriguez-Lozano, E. Del Rio, and M. G. Velarde, Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, 669 (1992).
22. R. C. Elson (private communication).
23. A. Szücs (private communication).
24. R. M. Harris-Warrick et al., in Dynamic Biological Networks: The Stomatogastric Nervous System,edited by R. M. Harris-Warrick et al. (MIT Press, Cambridge, MA, 1992).
25. Y. Yarom, Neuroscience 44, 263 (1999).
26. S. Renaud-Le Masson, E. Marder, G. Le Masson, and L. Abbott, Neural Information Processing Systems 5 (Morgan Kaufmann San Mateo, CA, 1993), pp. 813–819
27. G. Le Masson, S. Le Masson, and M. Moulins, Prog. Biophys. Mol. Biol. 64, 201 (1995).
28. A. Laflaquiere, S. Le Masson, J. P. Dom, and G. Le Masson, in Proceedings of the International Conference on Neural Networks (ICNN’97), Houston, TX, June, 1997 (IEEE, New York, 1997), Vol. 2, pp. 882-7
29. D. Dupeyron, S. Masson, Y. Deval, G. Le Masson, and J.-P. Dom, in Proceedings of the Fifth International Conference on Microelectronics for Neural Networks and Fuzzy Systems, MicroNeuro96, Lausanne, Switzerland, February, 1996 (IEEE Compututer Society, Los Alamitos, CA, 1996), pp. 311–16
30. S. Le Masson, Y. Deval, G. Le Masson, J. Tomas, D. Dupeyron, and J. P. Dom, in Proceedings of the Fourth International Conference on Microelectronics for Neural Networks and Fuzzy Systems, Turin, Italy, September, 1994 (IEEE Computer Society, Los Alamitos, CA, 1994), pp. 202–6.
31. An excellent introduction to the issues involved, the approximations employed, the methods of implementation as well as to the results of some experiments can be found in the dissertation of G. Le Masson available online at www.ixl-u-bordeaux.fr/equipes-ixl/neurone/Publications/These_Gwendal