The bistable Duffing oscillator in discrete time

The dynamics of an oscillatory system with a soft cubic-nonlinear return force - a bistable Duffing oscillator, in discrete time are consider. The mathematical analysis is based on a continuous-time model in the form of the Duffing equation. The transition to discrete time in the equation is performed using the Green function of linear oscillations in the vicinity of the minima of the bistable potential. This approach to sampling allowed us to introduce a new version of a nonlinear dynamic system - the bistable discrete Duffing oscillator. It is shown that the bistable discrete Duffing oscillator adequately reproduces the characteristics of regular and chaotic oscillations of the analog prototype.