This paper extends the bifurcation and stability analysis of the autonomous system considered in Part 1 to the case of a corresponding nonautonomous system. The effect of an external harmonic excitation on the Hopf bifurcation is studied via a modified Intrinsic Harmonic Balancing technique. It is observed that a shift in the critical value of the parameter occurs due to the external excitation. The analysis is carried out with the aid of MAPLE which is also instrumental in verifying the consistency of the approximations conveniently.

1.
Takens
F.
,
1973
, “
Normal Forms for Certain Singularities of Vector Fields
,”
An. Inst. Fourier
, Vol.
23
, pp.
163
195
.
2.
Bogdanov
R. I.
,
1981
, “
Versal Deformations of a Singular Point of a Vector Field on the Plane in the Case of Zero Eigenvalues
,”
Sel. Math. Sov.
, Vol.
1
, pp.
389
421
.
3.
Huseyin, K., and Wang, S., 1993, “On the Analysis of Non-linear Systems With Multiple Frequency Excitations,” Proceedings of the Hellenic Society for Theoretical Applied Mechanics 3rd National Congress, June 25–27, 1992, pp. 110–117.
4.
Huseyin, K., 1986, Multiple-Parameter Stability Theory and Its Applications. Oxford University Press, Oxford.
5.
Yu
P.
, and
Huseyin
K.
,
1986
, “
Static and Dynamic Bifurcations Associated with a Double Zero Eigenvalue
,”
Dynamic and Stability of System
, Vol.
1
, pp.
73
86
.
6.
Huseyin, K., 1973, Vibrations and Stability of Multiple Parameter Systems, Sijtoff & Noordhoff, Alpphen aan den Rijn.
7.
Huseyin
K.
, and
Atadan
A. S.
,
1983
, “
On the Analysis of the Hopf Bifurcation
,”
Int. J., Eng. Sci.
, Vol.
21
, pp.
247
262
.
This content is only available via PDF.
You do not currently have access to this content.