Predicting period-doubling bifurcations and multiple oscillations in nonlinear time-delayed feedback systems

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

Volumn 45, Issue 7, 1998, Pages 759-763

  Berns, Daniel W ^a   Moiola, Jörge L ^a   Chen, Guanrong ^b  

^a UNIVERSIDAD NACIONAL DE LA PATAGONIA SAN JUAN BOSCO   (Argentina)

^b UNIVERSIDAD NACIONAL DEL SUR   (Argentina)

Author keywords

Harmonic balance approximation; Hopf bifurcation; Period doubling bifurcation; Time delayed feedback

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BIFURCATION (MATHEMATICS); DELAY CIRCUITS; FEEDBACK; GRAPH THEORY; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; MATRIX ALGEBRA; NEURAL NETWORKS; NONLINEAR SYSTEMS;

HARMONIC BALANCE EQUATIONS; HOPF BIFURCATION; PERIOD DOUBLING BIFURCATION; TIME-DELAYED CHUA CIRCUIT; TIME-DELAYED FEEDBACK;

CIRCUIT OSCILLATIONS;

EID: 0032115001     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.703844     Document Type: Article

References (17)

1. J. G. Milton, A. Longtin, A. Beuter, M. C. Mackey, and L. Glass, "Complex dynamics and bifurcations in neurology," J. Theoretical Biol., vol. 138, pp. 129-147, 1989.
2. J. Foss, A. Longtin, B. Mensour, and J. Milton, "Multistability and delayed recurrent loops," Phys. Rev. Lett., vol. 76, pp. 708-711, Jan. 1996.
3. M. C. Mackey and L. Glass, "Oscillations and chaos in physiological control systems," Science, vol. 197, pp. 287-289, 1977.
4. L. Glass and M. C. Mackey, "Pathological conditions resulting from instabilities in physiological control systems," Ann. N.Y. Acad. Sci., vol. 316, pp. 214-235, 1979.
5. P. E. Rapp, R. A. Latta, and A. I. Mees, "Parameter-dependent transitions and the optimal control of dynamical diseases," Bull. Mather. Sci., vol. 50, no. 3, pp. 227-253, 1988.
6. J. Bélair, L. Glass, U. an der Heiden, and J. Milton, "Dynamical disease: Identification, temporal aspects and treatment strategies of human illness," Chaos, vol. 5, no. 1, pp. 1-7, 1995.
7. S. A. Campbel, J. Bélair, T. Ohira, and J. Milton, "Complex dynamics and multistability in a damped harmonic oscillator with delayed negative feedback," Chaos, vol. 5, no. 4, pp. 640-645, Dec. 1995.
8. J. Wu, "Global continua of periodic solutions to some difference differential equations of neutral type," Tôhoku Math. J., vol. 45, pp. 67-88, 1993.
9. Y. Ueda, H. Ohta, and H. B. Stewart, "Bifurcations in a system described by a nonlinear differential equation with delay," Chaos, vol. 4, no. 1, pp. 75-83, 1994.
10. A. N. Sharkowsky, Yu. Maistrenko, P. Deregel, and L. O. Chua, "Dry turbulence from a time-delayed Chua's circuit," J. Circuits Syst. Comput., vol. 3, pp. 645-668, June 1993.
11. J. L. Moiola and G. Chen, Hopf Bifurcation Analysis-A Frequency Domain Approach. Singapore: World Scientific, 1996.
12. J. Bélair, S. A. Campbell, and P. van den Driessche, "Frustration, stability, and delay-induced oscillations in a neural network model," SIAM J. App. Math., vol. 56, no. 1, pp. 245-255, Feb. 1996.
13. J. Wu, "Symmetric bifurcations of FDEs: Theory and applications to neural networks with memory," in Differential Equations and Control Theory, Z. Deng, Z. Liang, G. Lu, and S. Ruan, Eds. New York: Marcel Dekker, 1996, pp. 407-419.
14. A. I. Mees and L. O. Chua, "The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems," IEEE Trans. Circuits Syst., vol. CAS-26, pp. 235-254, Apr. 1979.
15. R. Genesio and A. Tesi, "A harmonic balance approach for chaos prediction: Chua's circuit," Int. J. Bifurcation Chaos, vol. 2, no. 1, pp. 61-79, 1992.
16. M. Gilli and G. M. Maggio, "Predicting chaos through an harmonic balance technique: An application to the time-delayed Chua's circuit," IEEE Trans. Circuits Syst. I, vol. 43, pp. 872-874, Oct. 1996.
17. H. Lu and Z. He, "Chaotic behavior in first-order autonomous continuous-time systems with delay," IEEE Trans. Circuits Syst. I, vol. 43, pp. 700-702, Aug. 1996.