Dynamics of coupled generators of quasiperiodic oscillations: Different types of synchronization and other phenomena
A problem of synchronization of quasiperiodic oscillations is discussed in application to an example of coupled systems with autonomous quasiperiodic dynamics. Charts of Lyapunov exponents are presented that reveal characteristic domains on the parameter plane such as oscillator death, complete synchronization, phase synchronization of quasiperiodic oscillations, broadband synchronization, broadband quasiperiodicity. Features of each kind of dynamical behavior are discussed. Analysis of corresponding bifurcations is presented, including quasiperiodic Hopf bifurcations, saddle–node bifurcations of invariant tori of different dimensions, and bifurcations of torus doublings. Both the case of dominance of quasiperiodic oscillations in one of the generators and the case of pronounced periodic resonances embedded in the region of quasiperiodicity are considered.