Reality of Chaos in Four-Dimensional Hysteretic Circuits

IEEE Transactions on Circuits and Systems

Volumn 38, Issue 12, 1991, Pages 1517-1524

  Saito, Toshimichi ^a  

^a HOSEI UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; HYSTERESIS; MATHEMATICAL TECHNIQUES - EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL TECHNIQUES - MATRIX ALGEBRA;

CIRCUIT DYNAMICS; FOUR-DIMENSIONAL HYSTERETIC CIRCUITS; HYSTERESIS SWITCHINGS; JACOBI MATRIX; JORAN MATRIX; SYMMETRIC 3D LINEAR EQUATIONS;

ELECTRIC NETWORKS, NONLINEAR;

EID: 0026390415     PISSN: 00984094     EISSN: None     Source Type: Journal    
DOI: 10.1109/31.108504     Document Type: Article

References (15)

1. T. Saito, “An approach toward higher-dimensional hysteresis chaos generators,” IEEE Trans. Circuits Syst., vol. 37, pp. 399–409, 1990.
2. T. Matsumoto, L.O. Chua, and K. Kobayashi, “Hyperchaos: Laboratory experiment and numerical confirmation,” IEEE Trans. Circuits Syst., vol. CAS-33, 11, pp. 1143–1147, 1986.
3. T. Matsumoto, L.O. Chua, and K. Ayaki, “Reality of chaos in the double scroll circuit: A computer-assisted proof,” IEEE Trans. Circuits Syst., vol. CAS-35, pp. 909–925, 1988.
4. R. Newcomb and N. Elleithy, “Chaos generation using binary hysteresis,” Circuits Syst. Signal Process, vol. 5, pp. 321–341, 1986.
5. T. Saito, “On chaos generator described by a piecewise-linear constrained equation,” Trans. IEICE, vol. J71-A, pp. 965–972, 1988.
6. I. Shimada and T. Nagashima, “A numerical approach to ergodic problem of dissipative dynamical systems,” Prog. Theor. Phys., vol. 61, pp. 1605–1616, 1979.
7. J.D. Farmer, E. Otto, and J.A. Yorke, “The dimension of chaotic attractors,” Physica, vol. 7D, pp. 153–180, 1983.
8. E.N. Lorenz, “The local structure of a chaotic attractor in four dimensions,” Physica, vol. 13D, pp. 90–104, 1984.
9. E.N. Lorenz, “Lyapunov numbers and the local structure of attractors,” Physica, vol. 17D, pp. 279–294, 1985.
10. J.L. Hudson, O.E. Rssler, and H.C. Killory, “Chaos in a four-variable piecewise-linear system of differential equations,” IEEE Trans. Circuits Syst., vol. CAS-35, vol. 7, pp. 902–908, 1988.
11. T. Endo and T. Narita, “Bifurcation route from two periodic solutions to chaos in a nonlinear system of two-degree of freedom,” Trans. IEICE, vol. J71-A, pp. 1752–1755, 1988.
12. T. Yoshinaga and H. Kawakami, “Codimension two bifurcation in nonlinear circuits with periodically forcing term,” Trans. IEICE, vol. J72-A, pp. 1821–1828, 1989.
13. P. Chossat and M. Golubitsky, “Symmetric-increasing bifurcation of chaotic attractors,” Physica D, vol. 32, pp. 423–436, 1988.
14. C.A. Jones, N.O. Weiss, and F. Cattaneo, “Nonlinear dynamos: A complex generalization of the Lorenz equations,” Physica, vol. 14D, pp. 161–176, 1985.
15. E.N. Lorenz, “Deterministic nonperiodic flow,” J. Atoms. Sci., vol. 20, pp. 130–141, 1963.