Dynamics of a Quasiperiodically-Forced Mathieu Oscillator

Mathieu’s equation [6], $$ \ddot x\, + \,(\delta \,\, + \,\,\varepsilon \,\cos \,t)\,x\, = \,0, $$ (1) is the paradigm for problems in parametric excitation in which an autonomous linear structure is driven by a periodic forcer, usually in a direction perpendicular to the direction of motion (e.g., the vertically forced pendulum, dynamic buckling of an elastic column, water waves in a vertically driven channel).