A comparative study of conditions for chaos onset in Duffing-type weakly and strongly nonlinear oscillators is carried out. Quasiperiodically forced oscillators with combined parametric and external excitation are considered. The concept of induced saddle states is introduced in order to illuminate reasons for chaos arising in weakly nonlinear systems. The conditions for, and the mechanisms of, the transition to chaos are investigated in detail, both analytically and numerically, for the case of weakly nonlinear oscillators. Multistability properties of the oscillators are studied as well. An important application of the theory is the stability analysis of parametric amplifiers. © 1996 The American Physical Society.

• Received 13 April 1995

DOI:https://doi.org/10.1103/PhysRevE.53.103