Stability analysis of degenerate hopf bifurcations for discrete-time systems

Latin American Applied Research

Volumn 33, Issue 4, 2003, Pages 413-418

  D'Amico, M B ^a   Paolini, E E ^b   Moiola, J L ^a,c  

^a Facultad de Ciencias Naturales e Instituto M Lillo   (Argentina)

^b UNIVERSIDAD NACIONAL DEL SUR   (Argentina)

^c UNIVERSITY OF COLOGNE   (Germany)

Author keywords

Discrete time nonlinear systems; Frequency domain; Harmonic balance method; Hopf bifurcation; Stability index

Indexed keywords

APPROXIMATION THEORY; BIFURCATION (MATHEMATICS); FREQUENCY DOMAIN ANALYSIS; HARMONIC ANALYSIS;

DISCRETE-TIME SYSTEMS;

NONLINEAR SYSTEMS;

EID: 0142085678     PISSN: 03270793     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (16)

1. Allwright, D. J., "Harmonic balance and the Hopf bifurcation theorem," Math. Proc. of Cambridge Phil. Soc. 82, 453-467 (1977).
2. Balibrea, F. and J. C. Valverde, "Bifurcations under nondegenerated conditions of higher degree arid a new simple proof of the Hopf-Neimark-Sacker Bifurcation Theorem," J. of Math. Analysis and Applications 237, 93-105 (1999).
3. Bi, Q. and P. Yu, "Double Hopf bifurcations and chaos of a nonlinear vibration system," Nonlinear Dynamics 19, 313-332 (1999).
4. D'Amico, M. B., J. L. Moiola and E. E. Paolini, "Hopf bifurcation for maps: A frequency domain approach," IEEE Trans. on Circuits and Systems- I 49, 281-288 (2002).
5. D'Amico, M. B., E. E. Paolini and J. L. Moiola, "On the stability of Hopf bifurcation for maps," Proc. Workshop NOES'2001, Delft, The Netherlands, 209-212 (2001).
6. Frouzakis, C. E., R. A. Adomaitis, and I. G. Kevrekidis, "Resonance phenomena in an adaptively-controlled system," Int. J. of Bifurcation and Chaos 1, 83-106 (1991).
7. Glendinning, P., Stalility, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations, Cambridge University Press, New York (1994).
8. Iooss, G., Bifurcations of Maps and Applications, Mathematical Studies 36, North Holland. Amsterdam (1979).
9. Kuznetsov, Y. A., Elements of Applied Bifurcation Theory, Springer Verlag, New York (1995).
10. Mees, A. I., Dynamics of Feedback Systems, John Wiley & Sons, Chichester (1981).
11. Mees, A. I. and L. O. Chua, "The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems," IEEE Trans. on Circuits and Systems 26, 235-254 (1979).
12. Moiola, J. L. and G. Chen, Hopf Bifurcation Analysis: A Frequency Domain Approach, World Sci. Series on Nonlinear Science A 21, World Scientific Publishing, Singapore (1996).
13. Peckham, B. B., C. E. Frouzakis and I. G. Kevrekidis, "Bananas and banana splits: A parametric degeneracy in the Hopf bifurcation for maps." SIAM J. Math. Anal. 26, 190-217 (1995).
14. Robinson, C., Dynamical Systems-Stability, Symbolic Dynamics, and Chaos, CRC Press, Boca Raton, USA (1999).
15. Shilnikov, L. P., A. L. Shilnikov, D. Turaev and L. O. Chua, Methods of Qualitative Theory in Nonlinear Dynamics-Part 2, World Scientific Publishing, Singapore (2001).
16. Whitley, D., "Discrete dynamical systems in dimensions one and two," Bull. London Math. Soc. 15, 177-217 (1983).