An Approach Toward Higher Dimensional Hysteresis Chaos Generators

IEEE Transactions on Circuits and Systems

Volumn 37, Issue 3, 1990, Pages 399-409

  Saito, Toshimichi ^a  

^a HOSEI UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICS; HYSTERESIS; MATHEMATICAL TECHNIQUES--EIGENVALUES AND EIGENFUNCTIONS; SYSTEM STABILITY;

CHAOS GENERATORS; HYPERCHAOS; LYAPUNOV EXPONENTS; POINCARE MAP; SINGULAR PERTURBATION THEORY;

ELECTRIC NETWORKS, NONLINEAR;

EID: 0025405332     PISSN: 00984094     EISSN: None     Source Type: Journal    
DOI: 10.1109/31.52733     Document Type: Article

References (21)

1. A. S. Pikovski and M. I. Rabinovich, “Stochastic oscillation in dissipative systems,” Phys. D., vol. 2, pp. 8–24, 1981.
2. L. O. Chua, M. Komuro, and T. Matsumoto, “The double scroll family,” IEEE Trans. Circuits Syst., vol. CAS-33, pp. 1073–1118, 1986.
3. R. Newcomb and N. Elleithy, “Chaos generation using binary hysteresis,” Circuits Syst. Signal Process., vol. 5, no. 3, pp. 321–341, 1986.
4. F. M. A. Salam and S. S. Sastry, “Dynamics of the forced Josephson junction circuit-,” IEEE Trans. Circuits Syst., vol. CAS-32, pp. 784–796, 1985.
5. T. Endo and L. O. Chua, “Chaos from phase-locked loops,” IEEE Trans. Circuits Syst., vol. 35, pp. 987–1003, 1988.
6. T. Matsumoto, L. O. Chua, and R. Tokunaga, “Chaos via torus break down,” IEEE Trans. Circuits Syst., vol. CAS-34, pp. 240–253, 1987.
7. T. Saito, “On chaos generating circuits described by a piecewise-linear constrained equation,” Trans. IEICE Japan, vol. J71-A, no. 4, pp. 965–972, 1988.
8. T. Matsumoto, L. O. Chua, and K. Kobayashi, “Hyperchaos-,” IEEE Trans. Circuits Syst., vol. CAS-33, pp. 1143–1146, 1986.
9. J. L. Hudson, O. E. Rossler, and H. C. Killory, “Chaos in four-variable piecewise-linear system of differential equations,” IEEE Trans. Circuits Syst., vol. 35, 7, pp. 902–908, 1988.
10. O. E. Rossler, “Continuous chaos-,” Proc. N.Y. Acad. Sci., vol. 310, pp. 376–394, 1978.
11. V. I. Oceledic, “A multiplicative ergodic theorem: Lyapunov characteristic numbers for dynamical systems,” Trans. Moscow Math. Soc, vol. 19, pp. 197–231, 1968.
12. I. Shimada and T. Nagashima, “A numerical approach to ergodic problem of dissipative dynamical systems,” Prog. Theor. Phys., vol. 61, pp. 1605–1616, 1979.
13. J. D. Farmar, E. Ott, and J. A. Yorke, “The dimension of chaotic attractor,” Phys. ID, pp. 153–180, 1983.
14. K. Kaneko, “Transition from torus to chaos accompanied by frequency locking with symmetry breaking,” Prog. Theor. Phys., vol. 69, no. 5, pp. 1427–1442, 1983.
15. C. Grabogi, E. Ott, and J. A. Yorke, “Crisis, sudden changes in chaotic attractor and transient chaos,” Phys. ID, pp. 181–200, 1983.
16. Y. Kajitani and S. Shinoda, Network analysis. Tokyo, Japan: Japan Science and Technical, 1979.
17. A. Lasota and J. A. Yorke, “On the existence of the invariant measure for piecewise monotonic transformations,” Trans. Amer. Math. Soc, vol. 186, pp. 481–488, 1973.
18. S. S. Sastry and C. A. Desoer, “Jump behavior of circuits and systems,” IEEE Trans. Circuits Syst., vol. CAS-28, pp. 1109–1124, 1981.
19. G. Ikegami, “Singular perturbation in folliations,” Preprint series of Nagoya Univ., Japan, 1986.
20. M. Fukuhara, “Ordinary differential equation,” Iwanami-Zensyo, 116, (in Japanese).
21. T. Saito, “The hysteresis chaos generator family,” in 1988 IEEE ISCAS Proc, pp. 15–18, 1988.