It is a natural property of stochastic dynamical systems to exhibit several co-existing, metastable regimes in state space, alternating between order and chaos and, thereby, different time scales of predictability. Famous examples include various states in the transition to turbulent fluid flow or metastable chemical configurations. However, such transient stochastic phenomena cannot yet be rigorously described by classical random dynamical systems theory which focuses on an asymptotic description of order and chaos in globally simplified settings.

Advancing tools from dr. Engel’s previous research (see example references [1,2,3,4]), the team will introduce a new distinction into a localized and global analysis, enabling a rigorous approach to transient random dynamics. You will investigate localizations of the dynamics in appropriate subsets of the state space, analyzing stability and predictability of trajectories via (moment) Lyapunov exponents and their statistical fluctuations.The methods will crucially support the development of stochastic bifurcation theory. During the PhD, you will initially work on a pre-specified subproject of your choosing, which allows you to develop your knowledge of the topic and research skills. As you gain experience, you will increasingly shape your own research directions. You will collaborate closely with dr. Maximilian Engel and other team members, and connect with several (inter)national collaboration partners.

Tasks and responsibilities: 

• Conduct research within the specified project, as described above.

• Disseminate your research findings through publications in academic journals and through presentations at international conferences.

• Participate in relevant seminars and engage in research collaborations locally and/or internationally.

• Participate in the Faculty of Science PhD training program.

• Participate in the department’s educational programs, assisting in teaching and supervision of undergraduate or Master students.

• Complete and defend a PhD thesis within the appointment duration of four years.

Example references:

For the application, you are not expected to study the following references in depth, but you may look into them for a high-level impression of the style of research:

1. A. Blessing, A. Blumenthal, M. Breden and M. Engel. Detecting random bifurcations via rigorous enclosures of large deviations rate functions, Physica D: Nonlinear Phenomena, 476: 134617, 2025.

2. A. Blumenthal, M. Engel and A. Neamtu. On the pitchfork bifurcation for the Chafee-Infante equation with additive noise. Probability Theory and Related Fields, 187: 603-627, 2023.

3. M.M. Castro, D. Chemnitz, H. Chu, M. Engel, J.S.W. Lamb and M. Rasmussen. The Lyapunov spectrum for conditioned random dynamical systems, to appear in Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2024+.

4. M. Engel, J.S.W. Lamb and M. Rasmussen. Conditioned Lyapunov exponents for random dynamical systems. Transactions of the American Mathematical Society 372(9): 6343-6370, 2019.

We are looking for an enthusiastic and driven candidate who meets the following requirements:

Your experience and profile:

• Educational background: You should have a Master’s degree in mathematics, with some background in probability theory and analysis.

• Interests: You should have a strong interest in stochastic analysis and dynamical systems and their connections to scientific questions.

• Communication skills: You should have excellent written and verbal communication skills in English.

• Teamwork and independence: You should be highly motivated and committed to your research. While you should be able to work independently, you should also have a cooperative attitude and be willing to collaborate with the team members or other researchers.

Knowledge of dynamical systems is a plus, as are extra-curricular activities in, for instance, student associations, sports, music, etc. Prior knowledge of random dynamical systems is beneficial, but not required.

A temporary contract for 38 hours per week for the duration of 4 years (the initial contract will be for a period of 18 months and after satisfactory evaluation it will be extended for a total duration of 4 years). The preferred starting date is between September 1, 2025 and January 1, 2026. This should lead to a dissertation (PhD thesis). We will draft an educational plan that includes attendance of courses and (international) meetings. We also expect you to assist in teaching undergraduates and master students.

The gross monthly salary, based on 38 hours per week, will range range from € 2.901 in the first year to €3.707 (scale P) in the last year. In addition, you will receive an 8% holiday allowance and 8,3% end-of-year allowance. The Collective Labour Agreement of Universities of the Netherlands is applicable.