Analysis and Control of Multistability in Non-Smooth Dynamical Systems.

Location: Streatham Campus, University of Exeter, EX4 4QJ

Project description:
Multistability has been observed in a broad range of engineering applications, and in some cases the coexisting stable solutions appear to be ‘’hidden’’, due to the complex structure of the basins of attraction (BoA). From a computational point of view, if the BoA for an attractor does not intersect with small neighborhoods of equilibria, this attractor is called a hidden attractor. Otherwise, it is called a self-excited attractor.

There is no regular way to predict the existence or coexistence of “hidden” attractors in a system since their BoA are not connected with unstable equilibria. So, one cannot guarantee the localization of a “hidden” attractor by following its trajectories with random initial conditions as its BoA could be very small.

The analysis and control of non-smooth dynamical systems is an on-going research, but there are very few studies for exploring such “hidden” dynamics in non-smooth dynamical systems. Investigation of “hidden” attractors is vital for engineering applications, since they may cause unexpected and potentially disastrous responses resulting in costly failure.

This project aims to investigate “hidden” coexisting attractors in non-smooth dynamical systems, and develop a general control method for avoiding these “hidden” attractors. The following approaches will be carried out for the project: (1) to investigate the bifurcation mechanisms in non-smooth systems by using an impact oscillator or a stick-slip oscillator; (2) to develop a systematic method for searching coexisting “hidden” attractors in non-smooth systems; (3) to develop a generalized control method to avoid “hidden” attractors.

For more information about the project and informal enquiries, please contact the primary supervisor: Dr Yang Liu - [Email Address Removed]


Entry requirements:
Applicants for this research project must have obtained, or be about to obtain, a First or Upper Second Class UK Honours degree, or the equivalent qualifications gained outside the UK, in an appropriate area of science or technology.
If English is not your first language you will need to meet the English language requirements and provide proof of proficiency.