Bifurcation in a parametrically excited two-degree-of-freedom nonlinear oscillating system with 1:2 internal resonance (Q1975405)

The authors examine the nonlinear response of a two-degree-of-freedom nonlinear oscillating system to parametric excitation in the case of 1:2 internal resonance, and study the principal parametric resonance with respect to the lower mode. The method of multiple scales is used to derive four first-order autonomous ordinary differential equations for the modulation of amplitudes and phases. The authors investigate the steady-state solutions of the modulated equations and their stability. The trivial solutions become unstable through pitchfork bifurcation, giving rise to coupled mode solutions. The Melnikov method is used to study the global bifurcation behavior, and the critical parameter is determined at which the dynamical system possesses a Smale horseshoe-type chaos.