Three-dimensional numerical modelling of temporal and spatial pattern formation in a dc-driven gas discharge-semiconductor system

A three-dimensional numerical model is developed and applied to study the temporal and spatial pattern formation in the planar layered system, consisting of a glow discharge layer, coupled to a high ohmic semiconductor layer. The whole system is sandwiched between two planar electrodes, to which a dc voltage is applied. In the case of temporal oscillations that occur in a transversely homogeneous mode, a bifurcation diagram as well as a Lorenz map are derived, demonstrating the transition of the system to chaos through a period-doubling bifurcation cascade. The results of the fully three-dimensional time-dependent calculations agree well with the linear stability analysis within its range of validity. Beyond the initial transient regime, the numerical solution reproduces the way in which the Turing–Hopf instability of the homogeneous stationary state develops into the running wave, which can be identified through the moving bands observed in the experiment. (paper)