Analysis of a nonsynchronized sinusoidally driven dynamical system

A nonautonomous system, i.e. a system driven by an external force, is usual ly considered as being phase synchronized with this force. In such a case, the dynamical behavior is conveniently studied in an extended phase space w hich is the product of the phase space R-m of the undriven system by an ext ra dimension associated with the external force. The analysis is then perfo rmed by taking advantage of the known period of the external force to defin e a Poincare section relying on a stroboscopic sampling. Nevertheless, it m ay so happen that the phase synchronization does not occur. It is then more convenient to consider the nonautonomous system as an autonomous system in corporating the subsystem generating the driving force. In the case of a si nusoidal driving force, the phase space is Rm+2 instead of the usual extend ed phase space R-m x S-1. It is also demonstrated that a global model may t hen be obtained by using m + 2 dynamical variables with two variables assoc iated with the driving force. The obtained model characterizes an autonomou s system in contrast with a classical input/output model obtained when the driving force is considered as an input.