Welcome to Nonlinear Dynamics Team

The team leader is Lenka, who started to build a team with Veronika during her doctoral studies. Recently, Deeptajyoti joined the team with support from the Marie Skłodowska-Curie Actions fellowship. Two PhD students, Jakub and Jan, are also collaborating with the team. Currently, five bachelor and five master students are working under the supervision of the team members.

Our latest research focuses on synchronizations from the bifurcation point of view. We want to contribute with an understanding of the synchronized coupled neurons, Josephson junctions, population dynamics field, and seasonal model in ecology and epidemiology. We have noticed that the theory of bifurcations of limit cycles and the torus birth N-S bifurcation (Hopf-Hopf, respectively) is usually not used in applied research publications. One reason is that forced oscillations are usually studied as nonautonomous systems with harmonic driving. The unboundedness of phase variables in such models presents an open challenge for studying their bifurcations through standard numerical continuation techniques. Embedding into a higher dimensional space with forcing given by the master oscillator described by normal Hopf bifurcation form implies a stable continuation of bifurcation manifolds in Matcont and a good starting point to study the system dynamics.

Our team has international cooperation on topics related to the synchronized coupled neurons with prof. Hil Meijer, and topics related to Josephson junctions with prof. Andre Botha from UNISA.

Published on  October 13th, 2022