Abstract:
In order to study the global bifurcations and chaotic dynamics of the truncated sine-Gordon equation with damping and forced exciting, the two-mode truncated sine-Gordon equation is obtained by using the generalized asymptotic inertial manifold. Then, the method of multiple scales is used to find the averaged equations of the two-mode sine-Gordon equation in the case of the primary resonance and 1: 1 internal resonance. With the aid of theory of normal form, the explicit expression of normal form for the averaged equations associated with a pair of double-zero eigenvalues and a pair of pure imaginary eigenvalues is given by using Maple program. Finally, the global perturbation techniques are applied to this normal form to analyze the global bifurcations and chaotic dynamics. The chaotic motion of the two-mode sine-Gordon equation is also found by the numerical simulation.