Analysis and Control of Multistability in Non-Smooth Dynamical Systems. Self-funded PhD in Engineering Ref: 3088

About the Research Project

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

Academic Supervisors:  Dr Yang Liu

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 -


General Information

Information about current fees can be found here:

Information about possible funding sources can be found here:

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. Click here for more information and a list of acceptable alternative tests.

How to apply

You will be asked to submit some personal details and upload a full CV, covering letter and two academic references. Your covering letter should outline your academic interests, prior research experience and reasons for wishing to undertake this project. You may also be asked to upload verified transcripts of your most academic qualification.

If you have any general enquiries about the application process please email

Please quote reference 3088 on your application and in any correspondence about this project.


Application deadline:24th September 2018
Value:This project is self-funded
Duration of award:Not applicable
Contact: EMPS PGR Team