Tracking unstable steady states by large-amplitude low-frequency periodic modulation of a control parameter: Phase-space analysis

Inhibition of chaos in a dissipative nonlinear system that is slowly (nonre sonantly) modulated across an instability domain of a fixed-point solution is investigated in detail, considerably extending previous analyses. Compar ison is made between the evolution of the modulated system and the evolutio n of the steady-state solution in phase space as a function of the modulati on parameter. It is shown that tracking of the steady-state solution across the instability domain (which can be achieved for a wide domain of modulat ion frequencies) occurs in a nonintuitive way, as a result of the combinati on of two factors, which can be present in many nonlinear systems.