Nonlinear dynamics of parametrically driven particles in a Φ6 potential

摘要: A general parametrically excited mechanical system is considered. Approximate solutions are determined by applying the method of multiple time scales. It shown that only combination parametric resonance additive type possible for examined. For this case, existence and stability properties fixed points averaged equations corresponding to nontrivial periodic original investigated. Thus, emphasis placed on understanding chaotic behaviour extended Duffing oscillator in Φ6 potential under excitation a specific parameter choice. From Melnikov-type technique, we obtain conditions homoclinic or heteroclinic bifurcation. Our analysis carried out case triple well with double hump which does not lead unbounded motion; complemented numerical simulations from illustrate fractality basins attraction. The results show threshold amplitude moves upwards as intensity increases. Numerical including bifurcation diagrams, Lyapunov exponents, phase portraits Poincare maps shown.