A study about the relationship between the Volterra series and the perturbation method
Abstract
The perturbation method is one of the classical methods for solving weak nonlinear equations, and the Volterra series is a classical mathematical tool for modeling the systems with weak nonlinearity. It is revealed in this study that, for a forced polynomial nonlinear system, only when its derived linear system is a damped dissipative system, the steady output responses calculated by using the perturbation method and by using the Volterra series would coincide with each other. This means that the Volterra series is valid for modeling only the polynomial nonlinear systems whose derived linear system is a damped dissipative system.
