Distribution of sub and super harmonic solution of Mathieu equation within stable zone

The third stable region of the Mathieu stability chart, surrounded by one p-transition and one 27p-transition curve is investigated. It is known that the solution of Mathieu equation is either periodic or quasi-periodic when its parameters are within stable regions. Periodic responses occur when they are on a "splitting curve". Splitting curves are within stable regions and are corresponding to coexisting of periodic curves where an instability tongue closes. Distributions of sub and super-harmonics, as well as quasi-periodic solutions are analyzed using power spectral density method