This project is motivated by a growing recent interest in the non-smooth dynamics where various physical systems have been studied.

An archetypal oscillator called SD oscillator has nonlinearity which can be smooth or discontinuous depending on the value of the smoothness parameter. Physically this oscillator is similar to a snap-through truss system. It has properties of both a smooth and discontinuous system (at the limit), and it is the subject of our investigation.

Potentially a wealth of knowledge can be drawn from the well developed theory of continuous dynamics and transferred to non-smooth applications. Extensive numerical analysis has been carried out to explore behaviour of this system and it was found that the system exhibits complex co-existence of periodic attractors and also periodic solutions with a strange chaotic attractor. The attractor can deform in shape or bifurcate to a high period periodic attractor depending on the strength of damping, or even can become a chaotic sea with islands of quasi-periodic trajectories for zero damping. Various nonlinear dynamics tools were employed to study this system and a number of analytical approximations were obtained.

SD Oscillator Studies