Vasylenko H. Mathematical modelling of nonlinear processes of phase synchronization and chaos

The thesis is devoted to numerical-analytical modelling of the complex systems of phase synchronization, in particular -- model Kuramoto with discrete time and some one-dimensional maps that are obtained from this model under certain conditions. As further extension of this subject the dynamics of the Arnol'd map with external quasiperiodic forcing of small frequency is investigated. In the work possible dynamical states of the considered systems were classified and described in detail, types of the bifurcation mechanisms of appearance and preservation of the stable spaciotemporal structures were defined; regions of the phase synchronization and chaos in the system parameters space were obtained.