Global bifurcations of a taut string with 1:2 internal resonance

The global bifurcations of a taut string are investigated with the case of 1:2 internal resonance. The method of multiple scales is applied to obtain a system of autonomous ordinary differential equations. Based on the normal form theory, the desired form for the global perturbation method is obtained. Then the method developed by Kovacic and Wiggins is used to find explicit sufficient conditions for chaos to occur by identifying the existence of a Silnikov-type homoclinic orbit. Finally, numerical results obtained by using fourth-order Runge–Kutta method agree with the theoretical analysis at least qualitatively.