Transition Sets Of Strong And Nonlinear Resonance Of General Van Der Pol Equation With Parametric And External Excitations

Here modified L-P method and multiple scales method are used to solve transition sets of strong and nonlinear resonance of general van der pol equation with parametric and external excitations by parametric transformation, and bifurcation response equation and transition sets of superharmonic and subharmonic resonance with strong nonlinearity of general van der pol equation with parametric and external excitation are worked out. Besides, transition sets and bifurcation graphs are drawed to help to analysize the problems theoretically, such as system stability and the partition of permanent area. Conclusions show that the transition sets of general and nonlinear van der pol equation with parametric and external excitations are more complex than those of general and nonlinear van der pol equation only with parametric excitation, which is helpful for the qualitative and quantificationally reference of engineering and science applications.