On phase-locked motions associated with strong resonance

Yu, P.; Huseyin, K.

doi:10.1090/qam/1205939

Authors: P. Yu and K. Huseyin
Journal: Quart. Appl. Math. 51 (1993), 91-100
MSC: Primary 34C23
DOI: https://doi.org/10.1090/qam/1205939
MathSciNet review: MR1205939
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Abstract: This paper is concerned with the stability and bifurcation behaviour of a nonlinear autonomous system in the vicinity of a compound critical point characterized by two pairs of pure imaginary eigenvalues of the Jacobian. Attention is focused on the local dynamics of the system near-to-resonance. The methodology developed earlier for the bifurcation analysis into periodic and quasi-periodic motions (unification technique coupled with the intrinsic harmonic balancing) is extended to consider the stability and bifurcations of resonant cases. A set of simplified rate equations characterizing the local dynamics of the system is derived. These equations differ from those associated with nonresonant cases in that they are phase-coupled. Furthermore, the stability conditions of the phase-locked periodic bifurcation solutions are presented. All the results are expressed in explicit forms.

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