NONLINEAR ANALYSIS OF MATHIEU-DUFFING OSCILLATOR WITH INTERACTING PARAMETRIC AND EXTERNAL EXCITATION

The study investigates the nonlinear dynamic characteristics of Mathieu-Duffing oscillator with interacting
parametric and external excitation. The amplitude and frequency of interacting parametric and external
excitation are the control parameters for dynamic analysis. The fourth order Runge-kutta method in MATLAB
is utilized for numerical analysis. The dynamic behaviors are analyzed through phase plane and time history. It
is observed that at lower values of amplitude of pure parametric excitation, the system shows evolution of
periodic attractors and at higher values of amplitude of pure parametric excitation, the system shows evolution
of coexisting attractors . The separation between the coexisting attractors decreases with increase in the value of
amplitude of parametric excitation. It is also observed that the system shows evolution of multiperiodic
attractors at lower value of amplitude of interacting parametric and external excitation. With increase in the
values of amplitude of interacting parametric and external excitation, there is evolution of toroidal attractors.
With further increase in amplitude and phase angle of interacting parametric and external excitation, there is
evolution of coexisting attractors.