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Delayed feedback mechanisms

School of Mathematics and Physics | PHD
Applications are now CLOSED
Funding
Funded
Reference Number
MAP/2020/20
Application Deadline
14 February 2020
Start Date
1 October 2020

Overview

Many real world processes feed parts of their own outputs back to themselves as inputs. For instance, in the climate system there are mechanisms that can either amplify or diminish the effects of the initial drivers of climate. Since interactions between subsystems are often not instantaneous, predictive and faithful mathematical models of systems with feedback should incorporate past dependence. Indeed, delay differential equations are deterministic mathematical models of many history driven problems of practical importance [1, 2].

The phase space of delay differential equations is the Banach space of continuous functions
φ : [−1, 0] → R with the norm given by kφk = max−1≤t≤0 |φ(t)|. That is, delay differential
equations can be viewed as infinite dimensional dynamical systems. Although there is a wide
variety of analytical, geometric and computational techniques to study the dynamics delay
differential equations, there are many challenging open questions. For instance, the existence
of the numerically observed chaos in x0(t) = −µx(t) + px(t − τ )1 + x(t − τ )n,
x ∈ R, µ, p, n, τ > 0,

the so-called Mackey-Glass equation [3], has not been proved yet.
The aim of the project is to study the dynamics of nonlinear differential equations with
different types of time lags such as multiple, time-dependent and state-dependent. The student
should have attended courses on Linear Algebra and Complex Variables, Metric and Normed
Spaces, and Functional Analysis.

References
[1] Smith, H. L, An introduction to delay differential equations with applications to the life sciences, Springer
New York, 2011.
[2] Erneux, T. Applied delay differential equations Springer Science & Business Media, 2009.
[3] Mackey, M. C. and Glass, L., Oscillation and chaos in physiological control systems., Science,
197(4300):287-289, 1977.v

Funding Information

Project Summary
Supervisor

Dr Gabor Kiss


Mode of Study

Full-time: 3 years


Apply now Register your interest

Mathematics overview

The Mathematical Research Centre conducts world-class research in the following areas: Algebra, Analysis, Operator Algebras, Algebraic Topology, Topological Data Analysis, PDEs, Survival Analysis, Bayesian Networks, Data Analytics and Operational Research. It maintains vibrant international links with a large number of researchers around the globe and regularly hosts international conferences and research visitors.

List of researchers, their interests and upcoming PhD projects can be found at:
https://web.am.qub.ac.uk/wp/msrc/.


Mode of study / duration
Registration is on a full-time or part-time basis, under the direction of a supervisory team appointed by the University. You will be expected to submit your thesis at the end of three years of full-time registration for PhD, or two years for MPhil (or part-time equivalent).

Mathematics Highlights
Industry Links
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Career Development
  • Graduates from the School take up employment through a number of companies such as Allstate, AquaQ Analytics, Citigroup, Deloitte, PwC, Randox, Seagate and UCAS.
World Class Facilities
  • Since 2014, the School has invested over £12 million in new world-class student and staff facilities. Maths and Physics students now have their own teaching centre that opened in 2016 housing experimental physics laboratories, two large computer rooms for mathematical simulations and student study plus a student interaction area.
Key Facts

  • Students will have access to our facilities, resources and our dedicated staff. The School of Maths & Physics is one of the largest Schools in the University. Staff are involved in cutting-edge research that spans a multitude of fields.
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Course content

Research Information

Research Themes
Information on the research interests and activities of academics in the Mathematical Science Research Centre can be found at https://web.am.qub.ac.uk/wp/msrc/. These interests fit into the themes: Algebra, Analysis, Data Science, Optimization and Operational Research, Partial Differential Equations, Statistics, Topology and Geometry.

Career Prospects

Introduction
Mathematical and statistical skills are in great demand in the economy, particularly the advanced skills developed at the PhD level.

Employment after the Course
As well as continuing in research careers, our PhD graduates have also gone on to work in finance, computing, data analysis, management and teaching. Our advisors will be happy to provide further information on the career prospects arising from your chosen research area. Further information on careers can be obtained from the School and the Faculty.

People teaching you

Dr David Barnes
Postgraduate Advisor - Mathematical Sciences Research Centre

Email: d.barnes@qub.ac.uk

Professor Ivan Todorov
Director of Research - Mathematical Sciences Research Centre

Email: i.todorov@qub.ac.uk

Learning Outcomes

Course structure

0

Facilities
Students will enjoy the benefits of modern practical laboratories, extensive computer facilities and interactive spaces.

Entrance requirements

Graduate
The minimum academic requirement for admission to a research degree programme is normally an Upper Second Class Honours degree from a UK or ROI HE provider, or an equivalent qualification acceptable to the University. Further information can be obtained by contacting the School.

International Students

For information on international qualification equivalents, please check the specific information for your country.

English Language Requirements

Evidence of an IELTS* score of 6.0, with not less than 5.5 in any component, or an equivalent qualification acceptable to the University is required. *Taken within the last 2 years.

International students wishing to apply to Queen's University Belfast (and for whom English is not their first language), must be able to demonstrate their proficiency in English in order to benefit fully from their course of study or research. Non-EEA nationals must also satisfy UK Visas and Immigration (UKVI) immigration requirements for English language for visa purposes.

For more information on English Language requirements for EEA and non-EEA nationals see: www.qub.ac.uk/EnglishLanguageReqs.

If you need to improve your English language skills before you enter this degree programme, INTO Queen's University Belfast offers a range of English language courses. These intensive and flexible courses are designed to improve your English ability for admission to this degree.

  • Academic English: an intensive English language and study skills course for successful university study at degree level
  • Pre-sessional English: a short intensive academic English course for students starting a degree programme at Queen's University Belfast and who need to improve their English.

Tuition Fees

Northern Ireland (NI) £4,407
England, Scotland or Wales (GB) £4,407
Other (non-UK) EU £4,407
International £16,950

More information on postgraduate tuition fees.

Mathematics costs

There are no specific additional course costs associated with this programme.

Additional course costs

All Students

Depending on the programme of study, there may also be other extra costs which are not covered by tuition fees, which students will need to consider when planning their studies . Students can borrow books and access online learning resources from any Queen's library. If students wish to purchase recommended texts, rather than borrow them from the University Library, prices per text can range from £30 to £100. Students should also budget between £30 to £100 per year for photocopying, memory sticks and printing charges. Students may wish to consider purchasing an electronic device; costs will vary depending on the specification of the model chosen. There are also additional charges for graduation ceremonies, and library fines. In undertaking a research project students may incur costs associated with transport and/or materials, and there will also be additional costs for printing and binding the thesis. There may also be individually tailored research project expenses and students should consult directly with the School for further information.

How do I fund my study?
1.PhD Opportunities

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2.Doctoral Training Centres at Queen's

Queen's has eight outstanding competitive Doctoral Training Centres, with each one providing funding for a number of PhD positions and most importantly a hub for carrying out world class research in key disciplines.

3.PhD loans

The Government offers doctoral loans of up to £26,445 for PhDs and equivalent postgraduate research programmes for English- or Welsh-resident UK and EU students, £10,000 for students in Scotland and up to £5,500 for Northern Ireland students.

4.International Scholarships

Information on Postgraduate Research scholarships for international students.

Funding and Scholarships

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How to Apply

Apply using our online Postgraduate Applications Portal go.qub.ac.uk/pgapply and follow the step-by-step instructions on how to apply.

Find a supervisor

If you're interested in a particular project, we suggest you contact the relevant academic before you apply, to introduce yourself and ask questions.

To find a potential supervisor aligned with your area of interest, or if you are unsure of who to contact, look through the staff profiles linked here.

You might be asked to provide a short outline of your proposal to help us identify potential supervisors.