A SIMPLE CRITERION FOR THE OCCURRENCE OF CHAOS IN NONLINEAR FEEDBACK-SYSTEMS

A simple method to analyze the conditions far chaos to occur in a nonl inear control system having a cubic characteristic is investigated. Th e analysis is based on the following conjecture: if there exist multip le equilibrium points all of which are unstable and an unstable limit surface surrounding them, then a trajectory starting from the inside o f the limit surface may wander in state space, and this phenomenon may constitute chaos. The describing function method is applied and an al gebraic parameter condition for chaos is derived. The parameter region s for the occurrence of chaos are presented for several transfer funct ions. It is also shown that this method can be applied to a time lag s ystem. (C) 1998 Scripta Technica.