Finding a class of systems that develop strange attractors when driven

MackTuesday

I'm trying to find a class of 3-D systems of differential equations that reach a fixed point when not driven, and develop a strange attractor when driven strongly enough by a sinusoid or other periodic function. In fact I'd like to find all such systems, if feasible. I know that Duffing's system is like this in some cases. Maybe no one has the complete answer, but how would you start looking?