Hopf bifurcation of a three-dimensional system

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 15, Issue 5, 2005, Pages 1603-1614

  Liu, Xuanliang ^a   Han, Maoan ^a  

^a NONE

Author keywords

Bifurcation; Periodic orbit; Three dimensional system; Weak focus

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; INVARIANCE; LYAPUNOV METHODS; MATRIX ALGEBRA; PROBLEM SOLVING; THREE DIMENSIONAL;

HOPF BIFURCATION THEOREM; PERIODIC ORBIT; THREE-DIMENSIONAL SYSTEM; WEAK FOCUS;

BIFURCATION (MATHEMATICS);

EID: 22144461409     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127405012880     Document Type: Article

References (13)

1. Algaba, A., Merino, M., Freire, E., Gamero, E. & Rodriguenz-Luis, A. J. [2000] "On the Hopf-pitchfork bifurcation in the Chua's equation," Int. J. Bifurcation and Chaos 10, 291-305.
2. Bautin, N. N. [1952] "On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or center type," Mat. Sbornik (N.S.) 30, 181-196.
3. Chow, S. N. & Hale, J. K. [1982] Methods of Bifurcation Theory (Springer-Verlag, NY).
4. Farr, W. W., Li, C., Labouriau, I. S. & Langford, W. F. [1989] "Degenerate Hopf bifurcation formulas and Hilbert's 16th problem," SIAM J. Math. Anal. 20, 13-30.
5. Gasull, A., Guillamon, A. & Mañosa, V. [1997] "An explicit expression of the first Liapunov and period constants with applications," J. Math. Anal. Appl. 211, 190-212.
6. Golubitsky, M. & Langford, W. F. [1981] "Classification and unfoldings of degenerate Hopf bifurcations," J. Diff. Eqs. 41, 375-415.
7. Guckenheimer, J. & Holmes, P. J. [1983] Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, Berlin).
8. Hale, J. K. [1980] Ordinary Differential Equations (Robert E. Krieger, NY).
9. Han, M. & Zhu, D. [1994] Bifurcation Theory in Differential Equations (Coal Industry Publishing House, Beijing) (in Chinese).
10. Han, M. [2002] Theory of Periodic Solutions and Bifurcations of Dynamical Systems (Science Publishing House, Beijing) (in Chinese).
11. Han, M., Lin, Y. & Yu, P. [2004] "A study on the existence of limit cycles of a planar system with third-degree polynomials," Int. J. Bifurcation and Chaos 14, 41-60.
12. Kuznetsov, Y. A. [1995] Elements of Applied Bifurcation Theory (Springer, NY).
13. Liu, W. M., Levin, S. A. & Iwasa, Y. [1986] "Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological model," J. Math. Biol. 23, 187-204.