Bifurcation behavior of a superlattice model

We present a complete description of the stationary and dynamical behavior of semiconductor superlattices in the framework of a discrete drift model b y means of numerical continuation, singular perturbation analysis, and bifu rcation techniques. The control parameters are the applied DC voltage (phi) and the doping (nu) in nondimensional units. We show that the organizing c enters for the long time dynamics are Takens-Bogdanov bifurcation points in a broad range of parameters and we cast our results in phi-nu phase diagra m. For small values of the doping, the system has only one uniform solution where all the variables are almost equal. For high doping we nd multistabi lity corresponding to domain solutions and the stationary solutions may exh ibit chaotic spatial behavior. In the intermediate regime of the solution c an be time-periodic depending on the bias. The oscillatory regions are rela ted to the appearance and disappearance of Hopf bifurcation tongues which c an be sub- or supercritical. These results are in good agreement with most of the experimental observations and also predict new interesting dynamical behavior.