Dynamical origin for the occurrence of asynchronous hyperchaos and chaos via blowout bifurcations

Mechanism for the partial synchronization in three coupled chaotic systems

We investigate the dynamical mechanism for the partial synchronization in three coupled one-dimensional maps. A completely synchronized attractor on the diagonal becomes transversely unstable via a blowout bifurcation, and then a two-cluster state, exhibiting on-off intermittency, appears on an invariant plane. If the newly created two-cluster state is transversely stable, then partial synchronization occurs on the invariant plane; otherwise, complete desynchronization takes place. It is found that the transverse stability of the intermittent two-cluster state may be determined through the competition between its laminar and bursting components. When the laminar (bursting) component is dominant, partial synchronization (complete desynchronization) occurs through the blowout bifurcation. This mechanism for the occurrence of partial synchronization is also confirmed in three coupled multidimensional invertible systems, such as coupled He non maps and coupled pendula.