Periodic forcing provides a sensitive probe on the dynamics of the Lorenz system near the onset of chaos. The unstable limit cycle in the Lorenz system produced by Hopf bifurcation is found to stabilize beyond a critical amplitude of forcing. This extends the dynamical similarity of the Lorenz system to real hydrodynamics (unforced) up to the onset of turbulence. We study the routes to chaos in this forced system.

• Received 11 May 1984

DOI:https://doi.org/10.1103/PhysRevA.31.520