Slow periodic crossing of a pitchfork bifurcation in an oscillating system
The nonlinear Mathieu equation is investigated as a case study of damped oscillating systems with slowly varying forcing function. The phase portrait of the system changes qualitatively with time with a pitchfork bifurcation point involved. A Poincaré map is constructed in order to describe the dynamics of the system as it repeatedly crosses the bifurcation point. The averaging methods and asymptotic matching techniques connecting local solutions are employed. Numerical simulations are compared with maps obtained analytically.
scientific article; zbMATH DE number 1042565