Dissertation
Transition Graphs of Interacting Hysterons
Transition graphs capture the memory and sequential response of multistable media, by specifying their evolution under external driving.
- Author
- M.H. Teunisse
- Date
- 03 June 2026
- Links
- Thesis in Leiden Repository
Microscopically, collections of bistable elements, or hysterons, provide a powerful model for these materials, with recent work highlighting the crucial role of hysteron interactions. This dissertation introduces a general framework that links transition graphs and the microscopic parameters of interacting hysterons. We first introduce a systematic framework, based on so-called scaffolds, which structures the space of transition graphs and provides tools to deal with their combinatorial explosion. We then connect the topology of transition graphs to partial orders of the microscopic parameters. This allows us to understand the statistical properties of transition graphs, as well as determine whether a given graph is realizable, i.e. compatible with the hysteron framework. Having established this general framework, we zoom in on self-loops and multiperiodic resposnes, and show that these two periodic features are closely related. Finally, we discuss several subvariants of the hysteron model, where restrictions are placed either on the distance between individual switching thresholds, or on the coupling between hysterons. We show that the responses of interacting hysterons are simplified for these restricted models, and link these models to physically realizable systems. Altogether, this work provides insight into the various types of responses which can be modelled by interacting hysterons, and serves as a jumping-off point for further explorations of multistable media.