Periodic solutions of delay nonlinear system by multi-frequency homotopy analysis method

摘要

A two-degree-of-freedom coupled Duffing system with time delay is studied by a modified homotopy analysis method. First, a detailed calculation is given for the system. Second, single periodic and period-doubling solutions are obtained by solving the constructed nonlinear algebraic equation. Third, upon comparison of the periodic solution obtained by the multi-frequency homotopy analysis method with the numerical solutions obtained by the numerical method, it is found that the approximate solution agrees well with the numerical solution for the system. Finally, we discuss the convergence control parameters and convergence control function.