Multi-Frequency Homotopy Analysis Method for Coupled Van der Pol-Duffing System with Time Delay

This paper mainly studied the analytical solutions of three types Van der Pol-Duffing equations. For a system with parametric excitation frequency, we knew that ordinary homotopy analysis method would be unable to find solution. Thus, primarily used multi-frequency (MFHAM). First, MFHAM was introduced, and solution expressed by constructing auxiliary linear operators. Then, applied specific systems. We compared numerical obtained using Runge–Kutta verify correctness latter. Periodic solutions, without time delay, were also under same parameters. The results demonstrated it both effective correct use systems, which classical By comparison, proved for delay