Asymptotic formulas in nearly sinusoidal nonlinear oscillators

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 43, Issue 12, 1996, Pages 953-963

  Buonomo, Antonio ^a  

^a UNIVERSITY OF SALERNO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; FEEDBACK; HARMONIC ANALYSIS; ITERATIVE METHODS; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; NONLINEAR NETWORK ANALYSIS; NONLINEAR NETWORKS; PERTURBATION TECHNIQUES; WAVEFORM ANALYSIS;

FEEDBACK OSCILLATORS; SINUSOIDAL NONLINEAR OSCILLATORS;

OSCILLATORS (ELECTRONIC);

EID: 0030380912     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.545836     Document Type: Article

References (21)

1. L. O. Chua and Y. S. Tang, "Nonlinear oscillation via Volterra series," IEEE Trans. Circuits Syst., vol. CAS-29, pp. 150-168, Mar. 1982.
2. A. Buonomo, C. D. Bello, and O. Greco, "On the existence and uniqueness of stable quasisinusoidal oscillations," Int. J. Circuit Theory Applicat., vol 13, pp. 327-337, 1985.
3. _, "On the evaluation of higher harmonics in nearly sinusoidal oscillators," Int. J. Circuit Theory Applicat., vol. 21, pp. 85-92, 1993.
4. W. Mathis and G. Wettlaufer, "Lie series averaging for electrical oscillators and computer algebra," in Proc. 31st Midwest Symp. Circuits Syst., St. Louis, MO, 1988.
5. J. Kevorkian and J. D. Cole, Pertubation Methods in Applied Mathematics. New York: Springer-Verlag, 1981.
6. L. Cesari, Asymptotic Behavior and Stability Problems in Ordinary Differential Equations. Berlin: Springer, 1971.
7. A. A. Andronov, S. E. Khaikin, and A. A. Vitt, Theory of Oscillations. Oxford, U.K.: Pergamon, 1966.
8. A. H. Nayteh and D. T. Mook, Nonlinear Oscillations. New York: Wiley, 1979.
9. A. Buonomo, "A collocation algorithm for calculating the periodic solution of nonlinear oscillators," Int. J. Circuit Theory Applicat., vol. 20, pp. 107-116, 1992.
10. R. S. Sidorowicz, "General nonlinear equation for LMRC oscillators and its nearly sinusoidal solutions," Int. J. Circuit Theory Applicat., vol. 3, pp. 135-148, 1975.
11. B. Z. Kaplan, R. Saaroni, and B. Zuckert, "Analytical and experimental approaches for the design of low-distorsion Wien-bridge oscillators," IEEE Trans. Instrum. Measure., vol. IM-30, pp. 147-151, 1981.
12. N. K. Jain and K. Singhal, "Efficient computational algorithm for linear oscillator frequency sensitivities," in Proc. Inst. Elect. Eng., Oct. 1981, vol. 128, pt. G, pp. 273-276.
13. R. E. Stuffle and P. M. Lin, "New approaches to computer aided determination of oscillator frequency sensitivities," IEEE Trans. Circuits Syst., vol. CAS-27, pp. 882-892, 1980.
14. A. Borys, "Elementary deterministic theories of amplitude and frequency stability in feedback oscillators," IEEE Trans. Circuits Syst., vol. CAS-34, pp. 254-255, 1987.
15. [151 J. K. Hale, Ordinary Differential Equations. Malabar: Krieger, 1980.
16. C. Fabry, "Existence et stabilité de solutions périodiques pour des equations différentielles quasilinéares d'ordre n." Int. J. Nonlinear Mach., vol. 5, pp. 447-463, 1970.
17. Y. S. Tang, A. I. Mees, and L. O. Chua, "Hopf bifurcation via Volterra series," IEEE Trans. Automatic Contr., vol. AC-28, pp. 42-53, 1983.
18. A. Ushida, L. O. Chua, and T. Sugawara, "A substitution algorithm for solving nonlinear circuits with multi-frequency components," Int. J. Circuit Theory Applicat., vol. 15, pp. 327-355, 1987.
19. E. F. Mishchenko and N. Kh. Rozov, Differential Equations with Small Parameters and Relaxation Equations. New York: Plenum, 1980.
20. M. Abramowitz and I. A. Stegun, Eds., Handbook of Mathematical Functions. London, U.K.: Dover, 1972, p. 823.
21. R. A. Struble, Nonlinear Differential Equations. New York: McGraw-Hill, 1962.