Nonlinear dynamics in physical models: Simple feedback-loop systems and properties

Computer Music Journal

Volumn 23, Issue 3, 1999, Pages 18-34

  Rodet, Xavier ^a   Vergez, Christophe ^a  

^a Inst Rech Coord Acoustique M   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038550957     PISSN: 01489267     EISSN: None     Source Type: Journal    
DOI: 10.1162/014892699559869     Document Type: Article

References (40)

1. Bergen, A. R., and R. L. Franks. 1971. "Justification of the Describing Function Method." SIAM Journal of Control 9(4):568-589.
2. Chow, S. N., O. Diekmann, and J. Mallet-Paret. 1985. "Stability, Multiplicity, and Global Continuation of Symmetric Periodic Solutions of a Nonlinear Volterra Integral Equation." Japan Journal of Applied Mathematics 2(2):433-469.
3. Chow, S. N., and D. Green, Jr. 1983. "Some Results on Singular Delay-Differential Equations." In P. Fischer and W. R. Smith, eds. Chaos, Fractals and Dynamics. New York: Marcel Dekker, pp. 161-182.
4. Chow, S. N., J. Mallet-Paret, and J. A. Yorke. 1978. "A Homotopy Method for Locating all the Zeros of a System of Polynomials." In Functional Differential Equations and Approximation of Fixed Points, volume 730 of Lecture Notes in Mathematiques. Berlin: Springer-Verlag, pp. 77-88.
5. Chua, L. O. 1992. "A Zoo of Strange Attractors from the Chua's Circuit." Proceedings of the 35th Midwest Symposium on Circuits and Systems. Washington, DC, pp. 916-926.
6. Chua, L. O., M. Komuro, and T. Matsumoto. 1986. "The Double Scroll Family." IEEE Transactions on Circuits and Systems 33(11):1073-1118.
7. Chua, L. O., and G.-N. Lin. 1990. "Canonical Realization of Chua's Circuit Family." IEEE Transactions on Circuits and Systems 37(7):885-902.
8. Dieckmann, O., S. A. van Gils, S. M. V. Lunel, and H. O. Walther. 1995. "Delay Equations. Functional, Complex and Nonlinear Analysis." Applied Mathematical Sciences, vol. 110. Berlin: Springer-Verlag.
9. Fletcher, N. H., and T. D. Rossing. 1991. The Physics of Musical Instruments. Berlin: Springer-Verlag.
10. Hale, J. K. 1991. "Dynamics and Delays." In S. Busenberg and M. Martelli, eds. Delay Differential Equations and Dynamical Systems, vol. 1475 of Lecture Notes in Mathematics. Berlin: Springer-Verlag.
11. Idogawa, T., M. Shimizu, and M. Iwaki. 1992. "Acoustical Behaviors of an Oboe and a Soprano Saxophone Artificially Blown." Proceedings of the Symposium on Some Problems on the Theory of Dynamical Systems in Applied Science. Singapore: World Scientific, pp. 71-93.
12. Ivanov, A. F., and A. N. Sharkovsky. 1992. "Oscillations in Singularly Perturbed Delay Equations." In C. K. R. T. Jones, U. Kirchgraber, and H. O. Walther, eds. Dynamics Reported. Berlin: Springer-Verlag, pp. 164-224.
13. Keefe, D. 1992. "Physical Modeling of Wind Instruments." Computer Music Journal 16(4):57-73.
14. Madan, R. N. 1992 (Washington, DC, 9-12 Aug.). "Observing and Learning Chaotic Phenomena from Chua's Circuit." Proceedings of the 35th Midwest Symposium on Circuits and Systems, pp. 736-745.
15. Matignon, D., Ph. Depalle, and X. Rodet. 1992 (San Jose, California). "State-Space Models for Wind-Instrument Synthesis." Proceedings of the 1992 International Computer Music Conference. San Francisco: International Computer Music Association, pp. 273-276.
16. McIntyre, M. E., R. T. Schumacher, and J. Woodhouse. 1983. "On the Oscillations of Musical Instruments." Journal of the Acoustical Society of America 74(5):1325-1345.
17. Mees, A. I. 1981. Dynamics of Feedback Systems. New York: Wiley.
18. Mees, A. I., and L. Chua. 1979. "The Hopf Bifurcation Theorem and Its Applications to Nonlinear Oscillations in Circuits and Systems." IEEE Transactions on Circuits and Systems 26(4):235-254.
19. Rodet, X. 1992 (San Jose, California). "Nonlinear Oscillator Models of Musical Instrument Excitation." Proceedings of the 1992 International Computer Music Conference. San Francisco: International Computer Music Association, pp. 412-413.
20. Rodet, X. 1993a (Hamburg, 16-20 August). "Nonlinear Oscillations in Sustained Musical Instruments: Models and Control." Proceedings of the 1993 European Nonlinear Oscillation Conference Euromech. Berlin: Akademie Verlag.
21. Rodet, X. 1993b (Hawaii). "Applications of Chua's Circuit to Sound, Music and Musical Instruments." Proceedings of the 1993 International Symposium on Nonlinear Theory and its Applications. Hawaii: IEICE, pp. 105-110.
22. Rodet, X. 1993c. "Sound and Music from Chua's Circuit." Journal of Circuits, Systems and Computers 3(1):49-61. (Special issue: Chua's Circuit: A Paradigm for Chaos.)
23. Rodet, X. 1993d. "Models of Musical Instruments from Chua's Circuit with Time Delay." IEEE Transactions on Circuits and Systems, 40(10) 696-701. (Special issue: Chaos in Nonlinear Electronic Circuits.)
24. Rodet, X. 1993e (Tokyo). "Flexible yet Controllable Physical Models: A Nonlinear Dynamics Approach." Proceedings of the 1993 International Computer Music Conference. San Francisco: International Computer Music Association.
25. Rodet, X. 1994 (Copenhagen). "Stability/Instability of Periodic Solutions and Chaos in Physical Models of Musical Instruments." Proceedings of the 1994 International Computer Music Conference.: San Francisco: International Computer Music Association, pp. 386-393.
26. Rodet, X. 1995a (Banff, Canada). "One- and Two-Mass Model Oscillation for Voices and Instruments." Proceedings of the 1995 International Computer Music Conference. San Francisco: International Computer Music Association, pp. 207-214.
27. Rodet, X. 1995b (Las Vegas, Nevada). "Oscillation, Chaos and Control of Nonlinear Dynamical Models of Musical Instruments with Sustained Sound." Proceedings of the Nonlinear Theory and Applications Conference. Las Vegas: IEICE, pp. 367-370.
28. Rodet, X., and Ph. Depalle. 1990. "Modèles de Signaux et Modèles Physiques d'Instruments." Proceedings of the Colloquium Modèles Physiques, Création Musicale et Ordinateur, Grenoble, 1990. Paris: Editions de la Maison des Sciences de l'Homme, 1994, pp. 351-370.
29. Rodet, X., and Ph. Depalle. 1992 (San José, California). "A Physical Model of Lips and Trumpet." Proceedings of the 1992 International Computer Music Conference. San Francisco: International Computer Music Association, pp. 132-135.
30. Rodet, X., and C. Vergez. 1999. "Nonlinear Dynamics in Physical Models: From Basic Models to True Musical-Instrument Models." Computer Music Journal 23(3):35-49.
31. Saneyoshi, J., H. Teramura, and S. Yoshikawa. 1987. "Feedback Oscillations in Reed Woodwind and Brasswind Instruments." Acustica 62:194-210.
32. Schumacher, R. T. 1981. "Ab Initio Calculations of the Oscillations of a Clarinet." Acustica 48:71-85.
33. Sharkovsky, A. N., Yu. Mastrenko, Ph. Deregel, and L. O. Chua. 1993. "Dry Turbulence from a Time-Delayed Chua's Circuit." Journal of Circuits, Systems and Computers 3(2). (Special issue: Chua's Circuit: A Paradigm for Chaos.)
34. Shuxian, W. 1987. "Chua's Circuit Family." Proceedings of the IEEE 75(8):1022-1032.
35. Smith, J. O. 1986. "Efficient Simulation of the Reed-Bore and Bow-String Mechanism." Proceedings of the 1986 International Computer Music Conference. San Francisco: Computer Music Association, pp. 275-280.
36. Smith, J. O. 1996. "Physical Modeling Synthesis Update." Computer Music Journal 20(2):44-56.
37. Välimäki, V., M. Karjalainen, and T. I. Laakso. 1993 (Tokyo). "Modeling of Woodwind Bores with Finger Holes." Proceedings of the 1993 International Computer Music Conference. San Francisco: International Computer Music Association, pp.32-39.
38. Vidyasagar, M. 1978. Nonlinear System Analysis. Englewood Cliffs, New Jersey: Prentice-Hall.
39. Walther, H. O. 1989. "Hyperbolic Periodic Solutions, Heteroclinic Connections, and Transversal Homoclinic Points in Autonomous Differential Delay Equations." Memoirs of the American Mathematical Society 79(402): 104.
40. Wawrzynek, J. C. 1987. "VISI Concurrent Computation for Music Synthesis." PhD dissertation, California Institute of Technology, Pasadena, California.