An analytical approach to investigate the response and stability of Van der Pol-Mathieu-Duffing oscillators under different excitation functions

摘要

In this paper the chaotic behavior of Van der Pol-Mathieu-Duffing oscillator under different excitation functions is studied. Governing equation is solved analytically using a powerful kind of analytic technique for nonlinear problems, namely the 'homotopy analysis method', for the first time. Present solution gives an expression, which can be used in a wide range of time for all domain of response. Comparisons of the obtained solutions with numerical results show that this method is effective and convenient for solving this problem. Finally, by using obtained analytical solution the stability and response of system under different excitation functions and constant parameters are shown.