Effects of constant excitation on local bifurcation (Q944573)

The authors discuss the effect of constant external excitation in a weakly coupled system of two oscillators involving \(1:2\) internal resonances. In particular, the local bifurcation of double-mode periodic solutions is treated in the presence of nonlinear terms in the oscillator with lower frequency. It is shown that in the non-degenerate case, the constant excitation parameter can not only determine the type of the bifurcation but also control the single-mode or double-mode bifurcation.