The responses of nolinear reaction models to periodic forcing in parameter regions of steady-state multiplicity have been examined. Stroboscopic mappings and periodic stability (Floquet) theory were eployed to explore bifurcation phenomena and their dependence on forcing amplitude, frequency and mean. A common feature of such systems is the transition from one to three periodic states (two of them stable) in the amplitude-frequency plane when the mean falls within the multiple steady state region of the unforced system. Parameter regions of higher multiplicity were also observed in some systems. Periodic doubling cascades resulting in chaos frequently occurred in one or more stable responses, often occupying large regions of the excitation diagram. Typically, although not always, the period doubling curves extended to a cusp at zero frequency in the amplitude vs frequency bifurcation diagram. Postulations, supported by numerical evidence, have been made about the relationship between the observed forced behaviors and the autonomous characteristics of nonlinear ODE systems. There is apparently a strong correlation between the size of the period doubling ovals of the forced system and the degree of focal, as opposed to nodal, transient behavior inherent in the unforced system. © 1990.
