Coexistence of synchronization and desynchronization: Data-driven analysis of coupled network models Coexistence of synchronization and desynchronization: Data-driven analysis of coupled network models

Often systems based on simple rules can yield rich and complicated structure and behavior. A simple quadratic map, for example, can yield fractal geometry in space and chaotic motion in time. A further paradigm for this type of complexity are networks of coupled phase oscillators showing so-called chimera states. All oscillators in these networks are identical and coupled in an identical way. The system can therefore be described by a single-line differential equation. If one moves in such a system, it looks everywhere the same. In chimera states, however, this symmetry in the system’s structure is broken by its temporal evolution. The system falls apart into two groups. One group of oscillators rotates coherently at an almost constant frequency, while the remaining oscillators perform an irregular motion. This counter-intuitive segregation into synchronous and non-synchronous motion has been studied using analytical, numerical and experimental approaches. More recently many conceptual links between chimera states and different real-world phenomena were drawn. This includes some recent work of our nonlinear time series analysis group, where we discovered an intriguing analogy between the collapse of chimera states and epileptic seizures. We furthermore studied the interaction of chimera states across separate networks and showed that a simple driver-response coupling between networks can lead to so-called generalized and phase synchronization across networks while both networks maintain their inner segregation into synchronized and desynchronized domains (for more details see https://www.upf.edu/web/ntsa/publications-featured). The proposed project aims to continue in these lines of research. It involves the data-driven study of signals derived from networks in chimera states as well as biomedical data provided by clinical partners. The latter includes, but is not limited to, electroencephalographic recordings from epilepsy patients.
Both the implementation of the networks as well as the signal analysis is purely numerical. The programming language Matlab will be used for this purpose.  Analytical aspects can be added, but shall not be the main focus of this work. This thesis involves no laboratory or experimental work. The ideal candidate should have a background in physics, mathematics or related fields. Previous experience in the study of dynamical systems is a plus. The candidate will work in our nonlinear time series analysis group, an international team that puts a strong emphasis on well-organized supervision of its junior members and regular research activities such as journal clubs, project meetings, etc.