Bifurcation of a modified BVP circuit model for neurons generating rectangular waves

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Volumn E82-A, Issue 9, 1999, Pages 1729-1736

  Tsumoto, Kunichika ^a   Yoshinaga, Tetsuya ^a   Kawakami, Hiroshi ^a  

^a UNIVERSITY OF TOKUSHIMA   (Japan)

Author keywords

Bifurcation; Chaos; Homoclinic orbit; Modified BVP equation; Neuronal model

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; CIRCUIT OSCILLATIONS; MATHEMATICAL MODELS;

BONHOFFER-VAN DER POL (BVP) EQUATION;

NONLINEAR EQUATIONS;

EID: 0033184957     PISSN: 09168508     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. T. Yoshinaga, H. Kawakami, and K. Yoshikawa, "A circuit metaphor for nonlinear oscillation in a chemical system at a water-oil interface," IEICE, Trans. vol.J71-A, no.10, pp. 1843-1851, Oct. 1988.
2. H. Kawakami and T. Yoshinaga, "Codimension two bifurcation and its computational algorithm," in Bifurcation and Chaos: Theory and Applications, J. Awrejcewicz, ed., pp.97-132, Springer-Verlag Berlin Heidelberg, 1995.
3. K. Yoshikawa, S. Maeda, and H. Kawakami, "Various oscillatory regimes and bifurcations in a dynamical system at an interface," Ferroelectrics, vol.86, pp.281-298, 1988.
4. J. Honerkamp, G. Mutschler, and R. Seitz, "Coupling of a slow and a fast oscillator can generate bursting," Bill. Math. Biol. vol.47, pp.1-21, 1985.
5. Y.I. Arshavsky, T.G. Deliagina, G.N. Orlovsky, and Y.V. Panchin, "Control of feeding movements in the freshwater snail Planorbis corneus. II. Activity of isolated neurons of buccal ganglia," Experimental Brain Research, vol.70, no.2, pp.323-331, 1988.
6. S. Doi and S. Kumagai, "Slow-fast analysis of bifurcations in a multi-dimensional Bonhöffer-van der Pol neuronal model," Proc. NOLTA'97, vol.2, pp. 1193-1196, 1997.
7. A.L. Hodgkin and A.F. Huxley, "A qualitative description of membrane current and its applications to conduction and excitation in nerve," J. Physiol, vol.117, pp.500-544, 1952.
8. K. Saeki, Y. Yachi, and Y. Sekine, "A study on hardware model of extended version of the Bonhoeffer-van der Pol model," Proc. IEICE General Conference, p.27, 1998.
9. H. Fujitani and H. Kawakami, "Mutual synchronization of unidirectionally coupled sinusoidal oscillators," Proc. NOLTA'98, vol.1, pp.9-12, 1998.
10. H. Flanders, Differential Forms with Applications to the Physical Sciences, Academic Press Inc., New York, 1963.
11. H. Kawakami and Y. Ozaki, "Analysis of a separatrix loop in n-dimensional autonomous system," IECE Trans., vol.J67-A, no.11, pp.1098-1099, Nov. 1984.
12. T. Yoshinaga and H. Kawakami, "Bifurcation and chaotic state in forced oscillatory circuits containing saturable inductors," in Nonlinear Dynamics in Circuits, L. Pecora and T. Carroll, eds., pp.89-119, World Scientific, 1995.
13. H. Kawakami, "Bifurcation of periodic responses in forced dynamic nonlinear circuits: computation of bifurcation values of the system parameters," IEEE Trans. Circuits & Systems, vol.CAS-31, no.3, pp.246-260, 1984.
14. S. Doi and S. Sato, "The Global Bifurcation Structure of the BVP Neuronal Model Driven by Periodic Pulse Trains," Mathematical Bioscienccs, vol.125, pp.229-250, 1995.
15. T. Matsumoto, L.O. Chua, and M. Komuro, "The double scroll," IEEE Trans. Circuits & Systems, vol.CAS-32, pp.797-818, 1985.
16. T. Matsumoto, M. Komuro, H. Kokubu, and R. Tokunaga Bifurcations - Sights, Sounds and Mathematics, Springer-Verlag, Tokyo, 1993.
17. L.O. Chua, M. Komuro, and T. Matsumoto, "The double scroll family, Part I and II," IEEE Trans. Circuits & Systems, vol.CAS-33, pp.1072-1118, 1986.