Applications are invited from aspiring PhD students to work on the research project `Fingerprints' of wild chaos: from theory to practical relevance. Two PhD scholarships, providing student fees and support, are available and fully funded by a Marsden grant from the Royal Society of New Zealand.
Project description
What kinds of complex dynamics must be expected in a given model of a time-dependent process? This fundamental question in dynamical systems, of theoretical as well as practical relevance, motivates the proposed research. At its core is wild chaos – a new form of complicated behaviour beyond `classical chaos' – that can only arise in a dynamical system of sufficiently high dimension. The existence of wild chaos as an abstract phenomenon has been established relatively recently, but very little is known to date about its creation and destruction as system parameters are varied. In particular, there is a lack of suitable explicit examples and, moreover, numerical verification of the required geometric ingredients poses serious technical difficulties.
The two PhD student will join the research effort to uncover geometric `fingerprints' of wild chaos under the supervision by Professors Hinke Osinga and Bernd Krauskopf. At its core are important geometric objects, known as blenders and hetero-dimensional cycles. Advanced theoretical and numerical tools will be combined to discover novel mechanisms resulting in transitions from simpler to observable wild chaotic behaviour. This will be achieved in practical and parameter-dependent settings, well beyond the realm of abstract construction.
Students from all nationalities with a suitable higher degree in (Applied) Mathematics or related fields are eligible for these PhD positions. To ensure a better gender balance in the research group, female candidates are particularly encouraged to apply. The ideal candidate has demonstrable skills in some of the following:
Contact
The successful candidate will join the research team led by Professors Hinke Osinga and Bernd Krauskopf in the Department of Mathematics at the University of Auckland. Informal enquiries and expressions of interest are welcome by email addressed to h.m.osinga@auckland.ac.nz and/or b.krauskopf@auckland.ac.nz.
How to apply
Applications should be sent by email to Professor Hinke Osinga; your application should include a cover letter expressing their interest, along with a CV, academic record, and list of three potential referees. The scholarships are available from March 2023, although the exact, feasible start date is flexible and to be agreed with the successful candidate as appropriate. Applications will be considered until the positions are filled.