On the onset of quasi-periodic solutions in third-order nonlinear dynamical systems

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 15, Issue 10, 2005, Pages 3165-3180

  Genesio, R ^a   Ghilardi, C ^a  

^a UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Bifurcations; Harmonic balance techniques; Nonlinear dynamics; Quasi periodic solutions

Indexed keywords

EID: 29244482010     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127405014064     Document Type: Article

References (30)

1. Anishchenko, V. S., Safonova, M. A. & Chua, L. O. [1993] "Confirmation of the Afraimovich-Shilnikov torusbreakdown theorem via a torus circuit," IEEE Trans. Circuits Syst.-I 40, 792-800.
2. Basso, M., Genesio, R. & Tesi, A. [1997] "A frequency method for predicting limit cycle bifurcations," Nonlin. Dyn. 13, 339-360.
3. Celikovsky, S. & Chen, G. [2002] "On the generalized Lorenz canonical form and chaotic systems," Int. J. Bifurcation and Chaos 12, 1789-1812.
4. Chen, G. & Dong, X. [1998] From Chaos to Order. Methodologies, Perspectives and Applications (World Scientific, Singapore).
5. Chen, G. (ed.) [1999] Controlling Chaos and Bifurcation in Engineering Systems (CRC Press, Boca Raton).
6. Chen, G. & Ueta, T. (eds.) [2002] Chaos in Circuits and Systems (World Scientific, Singapore).
7. Chen, G. & Yu, X. (eds.) [2003] Chaos Control Theory and Applications (Springer-Verlag, Berlin).
8. Duchesne, L. [1993] "Using characteristic multiplier loci to predict bifurcation phenomena and chaos: A tutorial," IEEE Trans. Circuits Syst.-I 40, 683-688.
9. Eichorn, R., Linz, S. J. & Hanggi, P. [1998] "Transformations of nonlinear dynamical systems to jerky motion and its application to minimal chaotic flows," Phys. Rev. E58, 7151-7164.
10. Genesio, R. & Tesi, A. [1992a] "Harmonic balance approach for chaos prediction: Chua's circuits," Int. J. Bifurcation and Chaos 2, 129-136.
11. Genesio, R. & Tesi, A. [1992b] "Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems," Automatica 28, 531-548.
12. Huang, A., Pivka, L., Wu, C. W. & Franz, M. [1993] "Chua's equation with cubic nonlinearity," Int. J. Bifurcation and Chaos 6, 2175-2222.
13. Impram, S. T., Johnson, R. & Pavani, R. [2003] "On the structure of the solutions of a two-parameter family of three-dimensional ordinary differential equations," Int. J. Bifurcation and Chaos 13, 1287-1298.
14. Jordan, D. N. & Smith, P. [1987] Nonlinear Ordinary Differential Equations (Clarendon Press, Oxford).
15. Khalil, H. K. [2002] Nonlinear Systems, 3rd edition (Prentice-Hall, Englewood Cliffs).
16. Kuznetzov, Yu. A. [1995] Elements of Applied Bifurcation Theory (Springer-Verlag, NY).
17. Linz, S. [2000] "No-chaos criterion for certain jerk systems," Phys. Lett. A275, 204-210.
18. Lu, J., Chen, G. & Cheng, D. [2004] "A new chaotic system and beyond: The generalized Lorenz-like system," Int. J. Bifurcation and Chaos 14, 1507-1537.
19. Madan, R. A. (ed.) [1993] Chua's Circuit: A Paradigm for Chaos (World Scientific, Singapore).
20. Matsumoto, T., Chua, L. O. & Tokunaga, R. [1987] "Chaos via torus breakdown," IEEE Trans. Circuits Syst. 34, 240-253.
21. Mees, A. I. [1981] Dynamics of Feedback Systems (Wiley, NY).
22. Moiola, J. L. & Chen, G. [1996] Hopf Bifurcation Analysis: A Frequency Domain Approach (World Scientific, Singapore).
23. Nayfeh, A. H. & Balachandran, B. [1995] Applied Non-linear Dynamics (Wiley, NY).
24. Sprott, J. C. [1994] "Some simple chaotic flows," Phys. Rev. E50, R647-R650.
25. Sprott, J. C. & Linz, S. J. [2000] "Algebraically simple chaotic flows," Int. J. Chaos Th. Appl. 5, 3-22.
26. Starkov, K. & Chen, G. [2004] "Chaotification of polynomial and rational normal forms," Chaos Solit. Fract. 22, 555-571.
27. Thompson, J. M. T. & Stewart, H. B. [1986] Nonlinear Dynamics and Chaos (Wiley, NY).
28. Torrini, G., Genesio, R. & Tesi, A. [1998] "On the computation of characteristic multipliers for predicting limit cycle bifurcations," Chaos Solit. Fract. 9, 121-133.
29. Vanecek, A. & Celikosky, S. [1994] Control Systems, from Linear Analysis to Synthesis of Chaos (Prentice-Hall, Englewood Cliffs).
30. Vidyasagar, M. [1993] Nonlinear Systems Analysis, 2nd edition (Prentice-Hall, Englewood Cliffs).