A Qualitative Analysis of the Behavior of Dynamic Nonlinear Networks: Stability of Autonomous Networks

IEEE Transactions on Circuits and Systems

Volumn 23, Issue 6, 1976, Pages 355-379

  Chua, Leon O ^a   Green, Douglas N ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b PURDUE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRIC NETWORKS, NONLINEAR;

EID: 0016969249     PISSN: 00984094     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCS.1976.1084228     Document Type: Article

References (29)

1. R. K. Brayton and J. K. Moser, “A theory of nonlinear networks,” Quart. Appl. Math., vol. 22, pp. 1-33, 81-104, Apr. and July 1964.
2. C. A. Desoer and F. F. Wu, “Trajectories of nonlinear RLC networks: A geometric approach,” IEEE Trans. Circuit Theory, vol. CT-19, pp. 562-571, Nov. 1972.
3. L. O. Chua and R. A. Rohrer, “On the dynamic equations of a class of nonlinear RLC networks,” IEEE Trans. Circuit Theory, vol. CT-12, pp. 475-489, Dec. 1965.
4. T. E. Stern, Theory of Nonlinear Networks and Systems, An Introduction. Reading, MA: Addison-Wesley, 1965.
5. A. Willson, Jr., Nonlinear Networks: Theory and Analysis. New York: IEEE Press, 1975.
6. D. A. Calahan, Computer-Aided Network Design. New York: McGraw-Hill, 1972.
7. L. O. Chua and P. M. Lin, Computer-Aided Analysis of Electronic Circuits: Algorithms and Computational Techniques. Englewood Cliffs, NJ: Prentice-Hall, 1975.
8. B. Gopinath and D. Mitra, “When are transistors passive,” B.S.T. J., vol. 50, no. 8, pp. 2835-2847, Oct. 1971.
9. I. W. Sandberg, “Some theorems on the dynamic response of nonlinear transistor networks,” B.S.T.J., vol. 48, pp. 35-54, Jan. 1961.
10. C. Hayashi, Nonlinear Oscillation in Physical Systems, New York: McGraw-Hill, 1964.
11. T. Roska, “On the uniqueness of the time-domain solution of nonlinear dynamic networks and systems,” College of Engineering, University of California, Berkeley, CA, Memo ERL-M458, Aug. 7, 1974.
12. J. J. Schaeffer, “Contributions to the theory of electrical circuits with nonlinear elements,” Ph.D. dissertation, The Swiss Federal Institute of Technology, Zurich, Switzerland, 1956.
13. P. P. Varaiya and R. Liu, “Normal form and stability of a class of coupled nonlinear networks,” IEEE Trans. Circuit Theory, vol. CT-12, pp. 413-418, Dec. 1966.
14. L. O. Chua and D. N. Green, “Graph-theoretic properties of dynamic nonlinear networks,” IEEE Trans. Circuits and Systems, vol. CAS-23, pp. 292-312, May 1976.
15. “A qualitative analysis of the behavior of dynamic nonlinear networks: steady state solution of nonautonomous networks,” to be published in IEEE Trans. Circuits and Systems.
16. “Qualitative theory of dynamic nonlinear networks,” in Proc. Int. Symp. Nonlinear Oscillations, East Berlin, Germany, Sept. 8-13, 1975.
17. J. Millman and C. Halkias, Integrated Electronics: Analog and Digital Circuits and Systems. New York: McGraw-Hill, 1972.
18. W. Hahn, Stability of Motion. New York: Springer-Verlag, 1967.
19. L. O. Chua and D. N. Green, “A qualitative analysis of the behavior of nonlinear dynamic networks: stability of autonomous networks,” College of Engineering, University of California, Berkeley, CA, Memo ERL-M508, Apr. 18, 1975.
20. J. M. Ortega and W. C. Rheinboldt, Iterative Solutions of Nonlinear Equations in Several Variables. New York: Academic Press, 1970, pp. 165-169.
21. L. O. Chua, “Stationary principles and potential functions for nonlinear networks,” Journ. Franklin Institute, vol. 296, pp. 91-114, Aug. 1973.
22. R. Rockafellar, Convex Analysis. Princeton, NJ: Princeton Univ. Press, 1970.
23. J. La Salle and S. Lefschetz, Stability by Lyapunov's Direct Method, with Applications. New York: Academic Press, 1961.
24. R. K. Brayton, “Nonlinear Reciprocal Networks,” in Mathematical Aspects of Electrical Network Analysis, SIAM-AMS Proc. vol. 3, pp. 1-15, Amer. Math. Soc., 1971.
25. V. A. Pliss, Nonlocal Problems in the Theory of Oscillations, New York: Academic Press, 1966.
26. L. O. Chua and N. N. Wang, “On the application of degree theory to the analysis of resistive nonlinear networks,” Int. J. of Circuit Theory and Applications, to be published.
27. P. Hartman, Ordinary Differential Equations. New York: Wiley, 1964.
28. C. A. Desoer, Notes for a Second Course on Linear Systems. New York: Van Nostrand Reinhold, 1971.
29. “Continuous systems modeling program (CSMP): A digitally simulated analog computer on a DSC META-IV 16K computer with IBM 2250 interactive graphics package,” College of Engineering, University of California, Berkeley, CA, Memo ERL-M350, Aug. 1972.