Order and Chaos in a Third-Order RC Ladder Network with Nonlinear Feedback

IEEE Transactions on Circuits and Systems

Volumn 36, Issue 9, 1989, Pages 1221-1230

  Ogorzalek, Maciej J ^a  

^a AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TECHNIQUES--PIECEWISE LINEAR TECHNIQUES; OSCILLATORS; SYSTEM STABILITY;

BIFURCATION PHENOMENA; CHAOTIC ATTRACTORS; NONLINEAR FEEDBACK; THIRD-ORDER RC LADDER NETWORK; TRANSITION TO CHAOS;

ELECTRIC NETWORKS, NONLINEAR;

EID: 0024736290     PISSN: 00984094     EISSN: None     Source Type: Journal    
DOI: 10.1109/31.34668     Document Type: Article

References (17)

1. I. M. Burkin and G. A. Leonov, “On the existence of periodic solutions in a nonlinear system of third order,” Differencialnye Urownienia, vol. XX, no. 12, pp. 2036-2042, 1984 (in Russian).
2. P. Gaspard and G. Nicolis, “What can we learn from homoclinic orbits in chaotic dynamics?” J. Stat. Phys., vol. 31, no. 3, pp. 499-518, 1983.
3. P. Glendinning and c. T. Sparrow, “Local and global behavior near homoclinic orbits,” J. Stat. Phys., vol. 31, no. 5/6, pp. 645-696, 1983.
4. P. Grabowski, “Dissipative systems of the Lur'e type,” in Proc. Nat. Conf. Circuit Theory and Electronic Systems, Poznan, pp. 402-406, 1985 (in Polish).
5. “An application of Shil'nikov's theorem to linear systems with piecewise-linear feedback,” Proc. MIDIT Workshop “Coherence, Structure and Chaos,” Tech. Univ. Denmark, Lyngby, 1986.
6. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. New York-Berlin-Tokyo: Springer Verlag, 1986; second edition.
7. T. Matsumoto, L. O. Chua, and M. Komuro, “The double scroll bifurcations,” Int. J. Circuit Theory Appl., vol. 14, pp. 117-146, 1986.
8. M. J. Ogorzalek and P. Grabowski, “Chaotic motion in RC circuit with nonlinear feedback function,” in Proc. VIII Nat. Conf. Circuit Theory Electronic Systems, Poznan, pp. 367-371, 1985 (in Polish).
9. “On the design of RC oscillators with single nonlinear activeelement,” Proc. European Conf. Circuit Theory and Design. Prague, 1985, vol. 1, pp. 287-290.
10. M. J. Ogorzalek, “Some observations on chaotic motion in single loop feedback systems,” in Proc. 1986 IEEE Conf. Decision and Control, Athens, 1986, vol. 1, pp. 588-589.
11. “Chaotic regions from double scroll,” IEEE Trans. Circuits Syst., vol. CAS-34, pp. 201-203, 1987.
12. “Some properties of a chaos generator with RC-ladder network,” in Proc. Euro Conf. Circuit Theory and Des., Paris, France, vol. 2. pp. 519-524, 1987.
13. “Complex bifurcation structure and chaos producing mechanismin RC-ladder chaos generator,” to be published.
14. T. S. Parker and L. O. Chua, “The dual double scroll equation,” IEEE Trans. Circuits Syst., vol. CAS-34, pp. 1059-1073, 1987.
15. O. E. Roössler, “Continuous chaos: Four prototype equations.” Ann. New York Acad. Sci., vol. 316, pp. 376-392, 1979.
16. R. S. Sidorowicz, “An abundance of sinusoidal RC-oscillators.” Proc. Inst. Elect. Eng., vol. 119, no. 3, pp. 283-293, 1972
17. C. Tresser, “About some theorems of L. P. Shil'nikov,” Ann. Inst. Henri Poincareé, vol. 40, pp. 441-461, 1984.