Models with cross interactions between partial dynamical processes aiming to understand significant or abrupt dynamic changes.

Bifurcation analysis of nonlinear models is a powerful tool that has a practical use since it detects and explains dynamical changes. It allows a description of generally emerging phenomena dependent on parameters.

This project aims to understand significant or abrupt changes in dynamics of models related to cross-interactions between partial dynamical processes and study how these cross-interactions affect the system's behavior as a whole. The project covers three fields of applied nonlinear dynamics: population biology, neuroscience and epidemiology.

Uncovering the dynamics of coupled prey-predator models (population biology), which includes persistence and extinction of the populations in cross-interacting patches, the emergence of periodic and aperiodic attractors, emergence of chaos, comparison of dynamics of the coupled model and the uncoupled one.

Uncovering the dynamics of coupled neuronal subsystems with respect to possible/impossible abrupt dynamical changes and synchronized dynamics.

Uncovering dynamics of coupled epidemic subsystems with emphasis on dynamics of COVID-19 epidemics to understand connections between dynamics of local and global outbreaks, interacting of sub-populations of various mutations and even seasonal effects.

I expect following exploitation of the results: theoretical in mathematical biology (new knowledge in population biology, neuroscience and epidemiology), applied (new knowledge of suitable/unsuitable models with respect to bifurcations, qualitative dynamical changes and emerging nonlinear phenomena in real world systems), educational (models attract attention of students and facilitates study of difficult passages of abstract mathematics), and practical in applied mathematics.

Part of the project is to strengthen the team of Prof. Pibylov (MU), including connection with the research group of Prof. Meijer (UT) in the field of applications in models of neuronal synchronization towards their focal epilepsy research.