Effects of constant excitation on local bifurcation

Abstract

The effects of the constant excitation on the local bifurcation of the periodic solutions in the 1:2 internal resonant systems were analyzed based on the singularity theory. It is shown that the constant excitation make influence only when there exist some nonlinear terms, in the oscillator with lower frequency. Besides acting as main bifurcation parameter, the constant excitation, together with coefficients of some nonlinear terms, may change the values of unfolding parameters and the type of the bifurcation. Under the non-degenerate cases, the effect of the third order terms can be neglected.

Dynamic Analysis of the Smooth-and-Discontinuous Oscillator under Constant Excitation

“…Based on the singularity theory, the effects of the constant excitation on the local bifurcation of the periodic solutions in the 1:2 internal resonant systems were analyzed in Ref. [1]. The computation of a complete response of the first order circuit with constant excitation was discussed in Refs.…”

“…Obviously, the gravity of the oscillator is not considered in system (1). In this study, the effect of the constant excitation produced by gravity or another constant force is investigated.…”