Hysteresis and onset of chaos in periodically driven nonlinear drift waves

The driven/damped nonlinear drift equation delta phi / delta t+a delta 3 phi / delta t delta 2 y+c delta phi / delta y+f phi delta phi / delta y=- epsilon sin (Ky- Omega t)- gamma phi is solved numerically. In ( epsilon , Omega ) space the properties of the solutions repeat in a self-similar way in cells of decreasing size for Omega to 0. Within each cell there are regions of constant, periodic, doubly periodic, etc. or chaotic energy E(t) for t to infinity . Regions of Omega with a 'high' and a 'low' branch solution of E also exist simultaneously, which gives rise to hysteresis for cyclically varied epsilon . Hopf bifurcations may take place on both branches. The width of the hystereses depends on the initial conditions. The space dependence of phi and its spectral properties are also studied.