Nonlinear Dynamics Team

Veronika completed a research internship with Hinke Osinga. During the visit, she had the opportunity to discuss the group’s current research direction in coupled oscillators and to learn new techniques that may enrich its future development. These included isochrons, phase resetting curves (PRC), phase transition curves (PTC), and rotation numbers on the torus, as well as their role in shaping system dynamics, including dynamics on invariant tori and their destabilisation.

Lenka Přibylová presented the Nonlinear Dynamics Team at the research exhibition organized on the occasion of the International Day of Women and Girls in Science at the Faculty of Science, Masaryk University. The talk highlighted how nonlinear dynamical systems help uncover crucial transitions in complex phenomena ranging from physical systems to neuroscience. You can see the presentation here. See program.

In February, Jan Ševčík successfully defended his doctoral dissertation devoted to synchronization phenomena in dynamical systems from the bifurcation theory perspective. The work investigated synchronization and multistability in small and larger networks of coupled neurons, analyzing their collective dynamics through a rigorous dynamical-systems framework. In particular, it demonstrated that time-distributed external stimulation can induce multiplication of the dominant oscillatory frequency, providing a plausible mechanistic explanation for the increased incidence of VHFOs and UFOs observed experimentally near epileptogenic tissue. You can find the presentation here

The GAMU INTERDISCIPLINARY project on mathematical modeling of very and ultra-fast oscillations in EEG has been successfully completed, delivering major advances in understanding pathological high-frequency brain rhythms through phase-shifted synchronization in neuronal networks. During the project, five research articles were published (four in top-decile IF journals), two additional papers were accepted for publication, and several theses, software tools, and international collaborations were completed, significantly strengthening the Nonlinear Dynamics Team and laying the groundwork for future large-scale grants.

Veronika Eclerová received the GAMU Career Restart grant for the project Invariant Descriptors Across Bifurcation Boundaries, aimed at accelerating her research activities following a career break due to maternity leave.