Proefschrift
Moving Patterns and Underlying Structures in Noisy Systems
In this dissertation, moving patterns and underlying structures in physical systems are studied, with particular attention to the role of noise. Noise refers to small random perturbations that are always present in reality. We study their effects because noise can have major consequences on long as well as short timescales.
- Auteur
- M. van den Bosch
- Datum
- 18 juni 2026
- Links
- Thesis in Leiden Repository
The first part focuses on moving patterns in reaction–diffusion systems. An example of such a system is the Belousov–Zhabotinsky reaction, in which chemical substances both react with one another and spread through space. The interplay between these two mechanisms can give rise to moving patterns such as wavefronts and spirals. In this dissertation, we mathematically investigate how fast waves propagate, how long they remain visible, and to what extent they are stable under small random perturbations.
The second part focuses on systems with (stochastic) delayed feedback, with applications ranging from leukemia research to laser stability. These delays can produce complex and chaotic dynamics. We investigate underlying structures (invariant probability measures) that describe the long-term behaviour of these systems. In this way, order and balance can be revealed in dynamics that may at first sight appear unpredictable. Finally, we study how delayed feedback (Pyragas control) can set stationary patterns into motion.