Critical Cascades of Fast-slow Dynamical Systems - Mathematics - EPSRC DTP funded PhD Studentship Ref: 2931

About the award

This project is one of a number funded by the Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Partnership to commence in September 2018. This project is in direct competition with others for funding; the projects which receive the best applicants will be awarded the funding.

The studentships will provide funding for a stipend which is currently £14,553 per annum for 2017-2018. It will provide research costs and UK/EU tuition fees at Research Council UK rates for 42 months (3.5 years) for full-time students, pro rata for part-time students.

Please note that of the total number of projects within the competition, up to 15 studentships will be filled.

Professor Peter Ashwin
, University of Exeter

Streatham Campus, Exeter

Project Description
This funded PhD project will develop the mathematical theory of critical transitions, also known as tipping points. These are sudden changes in the state of a nonlinear dynamical system state, in response to a gradual change to input. They are often associated with bifurcations of a branch of quasi-static attractors, if a parameter is slowly varied through a critical value. However, it may also be associated with more subtle interactions of timescales with the system, where there is a critical rate instead of a threshold. The project will aim to develop computable criteria for the presence of rate-dependent critical transitions, based on analysis of geometric structures within phase space. Some criteria may be exact, while others will involve numerical approximation. In particular, the project will look at changes in structure of basins of attraction of quasi-static attractors and how this may or may not lead to a critical transition. Particular aspects that will be studied in the project are (a) the role of timescale separation within parts of the nonlinear system, (b) the geometry of basins of attraction and (c) the cascading of tipping points between coupled nonlinear systems of fast-slow type. Tools include pullback attractors for non-autonomous systems and geometric singular perturbation theory. There is potential for the student to be involved in ongoing collaborations for applications to climate system dynamics where it is important to understand interactions between various subsystems that may undergo tipping. It will suit a candidate with a background in mathematics and a strong interest in nonlinear dynamical systems, ordinary differential equations and mathematical modelling.

Entry Requirements
You should have or expect to achieve at least a 2:1 Honours degree, or equivalent, in Mathematics or a related field.

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.

The majority of the studentships are available for applicants who are ordinarily resident in the UK and are classed as UK/EU for tuition fee purposes.  If you have not resided in the UK for at least 3 years prior to the start of the studentship, you are not eligible for a maintenance allowance so you would need an alternative source of funding for living costs. To be eligible for fees-only funding you must be ordinarily resident in a member state of the EU.  For information on EPSRC residency criteria click here.

Applicants who are classed as International for tuition fee purposes are NOT eligible for funding. International students interested in studying at the University of Exeter should search our funding database for alternative options.


Application deadline:10th January 2018
Value:3.5 year studentship: UK/EU tuition fees and an annual maintenance allowance at current Research Council rate. Current rate of £14,553 per year.
Duration of award:per year
Contact: Doctoral

How to apply

You will be required to upload the following documents:
•       CV
•       Letter of application outlining your academic interests, prior research experience and reasons for wishing to
        undertake the project.
•       Transcript(s) giving full details of subjects studied and grades/marks obtained.  This should be an interim
        transcript if you are still studying.
•       If you are not a national of a majority English-speaking country you will need to submit evidence of your current
        proficiency in English.  For further details of the University’s English language requirements please see

The closing date for applications is midnight (GMT) on Wednesday 10 January 2018.  Interviews will be held at the University of Exeter in late February 2018.

If you have any general enquiries about the application process please email:
Project-specific queries should be directed to the supervisor.

During the application process, the University may need to make certain disclosures of your personal data to third parties to be able to administer your application, carry out interviews and select candidates.  These are not limited to, but may include disclosures to:

• the selection panel and/or management board or equivalent of the relevant programme, which is likely to include staff from one or more other HEIs;
• administrative staff at one or more other HEIs participating in the relevant programme.

Such disclosures will always be kept to the minimum amount of personal data required for the specific purpose. Your sensitive personal data (relating to disability and race/ethnicity) will not be disclosed without your explicit consent.