Computation of the simplest normal forms for resonant double Hopf bifurcations system based on lie transform

Transactions of Tianjin University

Volumn 12, Issue 3, 2006, Pages 180-185

  Zhang, Qichang ^a   He, Xuejun ^a   Hao, Shuying ^b  

^a TIANJIN UNIVERSITY   (China)

^b TIANJIN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Bifurcation; Computer program; Lie operator; Mathematical transformations; Nonlinear systems; Normal form

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTER PROGRAMMING; NONLINEAR SYSTEMS;

LIE OPERATOR; NONLINEAR TRANSFORMATIONS; NORMAL FORM; RESONANT DOUBLE HOPF BIFURCATIONS SYSTEM; SYSTEM MATRIX;

MATHEMATICAL TRANSFORMATIONS;

EID: 33747079817     PISSN: 10064982     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (10)

1. Wang X F, Chen G T, Wang D. Unique normal forms for the Takens-Bogdanov singularity in a special case [J]. C R Acad Sci, Paris, 2001, 332 (6): 551-555.
2. Yuan Y, Yu P. Computation of simplest normal forms of differential equations associated with a double-zero eigenvalue [J]. International Journal of Bifurcation and Chaos, 2001, 11 (5): 1307-1330.
3. Yu P, Yuan Y. The simplest normal form for the singularity of a pure imaginary pair and a zero eigenvalue [J]. Dynamics of Continuous, Discrete Impulsive Systems (DCDIS), Series B Applications and Algorithms, 2001, 8 (3): 219-249.
4. Yu P, Yuan Y. The simplest normal forms associated with a triple zero eigenvalue of indices one and two [J]. Special Issue of Nonlinear Analysis: Theory, Methods and Applications, 2001, 47 (2): 1105-1116.
5. Yu P. Computation of the simplest normal forms with perturbation parameters based on Lie transform and rescaling [J]. Journal of Computational and Applied Mathematics, 2002, 144 (2): 359-373.
6. Yu P, Leung A Y T. The simplest normal form of Hopf bifurcation [J]. Nonlinearity, 2003, 16 (1): 277-300.
7. Chen Yushu, Wu Zhiqiang. Normal form of the multiple Hopf bifurcations in the non-internal resonant cases [J]. Acta Mechanica Sinica, 1997, 29 (6): 669-675 (in Chinese).
8. Zhang Q C, Leung A Y T. Normal form of double Hopf bifurcation in forced oscillators [J]. Journal of Sound and Vibration, 2000, 231 (4): 1057-1069.
9. Leung A Y T, Zhang Q C. Normal form computation without central manifold reduction [J]. Journal of Sound and Vibration, 2003, 266 (2): 261-279.
10. Yu P. Symbolic computation of normal forms for resonant double Hopf bifurcations using multiple time scales [J]. Journal of Sound and Vibration, 2001, 247 (4): 615-63.