Heteroclinic bifurcation in a quasi-periodically excited rigid rocking block with two frequencies

Abstract

Heteroclinic bifurcation in a nonlinear rigid rocking block under external quasi-periodic excitation with two frequencies is investigated. By using the method of Melnikov type, we derive sufficient conditions under which the perturbed stable and unstable manifolds of the heteroclinic orbits intersect transversally. Then a complete description of the bifurcation sets and the chaotic zones in the parameter space are presented. Numerical simulations are performed for parameters chosen from the chaotic zones. The chaotic motions of the system are verified by computing the largest Lyapunov exponent of the system.