Study on a new nonlinear parametric excitation equation: Stability and bifurcation

Anstract The parameter stability and global bifurcations of a strong nonlinear system with parametric excitation and external excitations are investigated in detail. Using the method of Multiple scales, the nonlinear system is transformed to the averaged equation. The parameter stability of solution in the case of principal parametric resonance is developed. Based on the averaged equation, the continuation algorithm is utilized to analyze the detailed bifurcation scenario as the parameter f0 is varied. The results indicate that there exist two limit points and neutral saddle points. Finally, a series of branching points were obtained by changing the parameters f0 and ρ.