Synchronisation and chaos in a parametrically and self-excited system withtwo degrees of freedom

Vibration analysis of a non-linear parametrically and self-excited system o f two degrees of freedom was carried out. The model contains two van der Po l oscillators coupled by a linear spring with a a periodically changing sti ffness of the Mathieu type. By means of a multiple-scales method, the exist ence and stability of periodic solutions close to the main parametric reson ances have been investigated. Bifurcations of the system and regions of cha otic solutions have been found. The possibility of the appearance of hyperc haos has also been discussed and an example of such solution has been shown .