Chaotic period-doubling and OGY control for the forced Duffing equation

In this paper we consider the Duffing equation forced with a pulse function, whose moments of discontinuity depend on the initial data. Existence of the chaos through period-doubling cascade is proved, and the OGY control method is used to stabilize the periodic solutions. Appropriate simulations of the chaos and stabilized periodic solutions are presented.

► The forced Duffing equation admits the chaos through period-doubling cascade.
► The discontinuity moments of the pulse function depend on the initial data.
► We prove existence of the chaos theoretically.
► Appropriate simulations including the bifurcation diagram are presented.
► The periodic solutions are stabilized by means of the OGY control method.