Return map quantization from an integrate-and-fire model with two periodic inputs

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Volumn E82-A, Issue 7, 1999, Pages 1336-1342

  Torikaü, Hiroyuki ^a   Saitqt, Toshimichi ^a  

^a HOSEI UNIVERSITY   (Japan)

Author keywords

Chaos; Computer aided analysis; Integrate and fire model; Quantization; Return map

Indexed keywords

CHAOS THEORY; COMPUTER AIDED ANALYSIS; MATHEMATICAL MODELS;

INTEGRATE-AND-FIRE (IFM) SYSTEMS; RETURN MAP QUANTIZATION;

DIGITAL SIGNAL PROCESSING;

EID: 0032596462     PISSN: 09168508     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. L. Glass and M.C. Mackcy, "A simple model for phase locking of biologicaloscillators," J. Math. Biology, vol.7, pp.339-352, 1979.
2. R. Pcrcz and L .Glass, "Bistability, period doubling bifurcations and chaos in a periodically forced oscillator," Phys. Lett. vol.OOA, no.9, pp.441-443, 1982.
3. J.P. Keener, F.C. Hoppensteadt, and J. Rinzel, "Integrateand-fire models of nerve membrane response to oscillatory input," SIAM J. Appl. Math., vol.41, pp.503-517, 1981.
4. A.R. Bulsara, T.C. Elston, C.R. Doering, S.B. Löwen, and K. Lindenberg, "Cooperative behavior in periodically driven noisy integratc-and-fire models of neuronal dynamics," Phys. Rev. E, vol.53, no.4, pp.3958-3969, 1996.
5. S. Sato, T. Shimokawa, K. Pakdaman, and T. Nomura, "Possible role of noise in sensory systems," Proc. 2nd RIEC Int. Symposium DAISP, pp.9-14, 1998.
6. [G] R.P. Pascual and J. Lomnitz-Adler, "Coupled relaxation oscillators and circle maps," Physica D 30, pp.Gl-82, 1988.
7. E. Catsigeras and R. Budelli, "Limit cycles of a bineuronal network model," Physica D 56, pp.235-252, 1992.
8. V. Kirn and E. Stone, "Effect of a refractory period on the entrainment of pulse-coupled integrate-and-fire oscillators," Phys. Lett. A, vol.232, pp.70-76, 1997.
9. H. Torikai and T. Saito, "A multiplex communication system using chaotic pulse-train with sawtooth control," Proc. IEEE Int. Symposium on Circuits and Systems, pp.1065-1068, 1997.
10. N.F. Rulkov and A.R. Volkovskii, "Threshold synchronization of chaotic relaxation oscillations," Phys. Lett. A, vol.179, pp.332-336, 1993.
11. H. Torikai, T. Saito, and W. Schwarz, "A chaotic pulse generator and sawtooth control for information processing," Proc. IEEE International Symposium on Circuits and Systems, pp.729-732, 1997.
12. M. Watanabe and K. Aihara, "What functional connectivity can do: Software driven neural networks," Proc. Int. Conf. on Neural Information Processing, pp.1370-1373, 1998.
13. J. Nagumo and S. Sato, "On a response characteristics of a mathematical neuron model," Cybernetik, vol.10, pp.155-164, 1972.
14. H. Torikai and T. Saito, "Computer aided analysis of chaotic oscillators with periodic perturbation," Proc. Int. Workshop on Nonlinear Dynamics of Electronic Systems, pp.75-78, 1998.
15. C.S. Hsu and R.S. Guttalu, "A universal algorithm for global analysis of dynamical systems: An application of cell-to-cell mappings," Trans. ASME, vol.47, pp.940-948, 1980.
16. F.C. Hoppensteadt, "Analysis and simulation of chaotic systems," Springer-Verlag New York, Inc., 1993.
17. A. Lasota and M.C. Mackey, "Chaos, Fractals, and Noise-Second Edition," Springer-Verlag, 1994.
18. T.Y. Li and J.A. Yorke, "Ergodic transformations from an interval into itself," Trans. Amer. Math. Soc., 235, pp.183-192, 1978.
19. E. Ott, "Chaos in Dynamical Systems," Cambridge Univ. Press, 1993.