The dynamics of a non-autonomous chaotic system with one cubic nonlinearity is studied through numerical and experimental investigations in this paper. A method for calculating Lyapunov exponents (LEs), Lyapunov dimension (LD) from time series is presented. Furthermore, some complex dynamic behaviors such as periodic, quasi-periodic motion and chaos which occurred in the system are analyzed, and a route to chaos, phase portraits, Poincare sections, bifurcation diagrams are observed. Finally, a first order differential controller for the non-autonomous system is designed. Also some dynamics such as Poincare sections, bifurcation diagrams for specific control parameter values of the controlled system are showed using numerical and experimental simulations.