Research on Extended Duffing Equation and its Dynamics

Duffing equation exhibits rich dynamics and has difficulties in numerical calculation and hardware design because of the nonlinear restoring force. This paper put forward a novel idea for extending the nonlinear Duffing equation to linear by the low order approximation of the double well potential, and researched the dynamics of the proposed equation. The numerical simulation results indicated that the proposed extended Duffing equation had the same dynamics with the original one. The linearization of Duffing equation brings many benefits in computational resources, operation speed, hardware designs efficiency, and so on, and provides a novel notion for the application of Duffing equation in the fields, such as system control and signal detection.