Fronts in a bistable medium with two global constraints: Oscillatory instability and large-amplitude limit-cycle motion

We study the propagation of fronts in a reaction-diffusion model of a bistable medium with two global constraints. The model applies to lateral current density fronts in three-electrode bistable semiconductor systems driven by the main and gate circuits. When taken separately, these constraints provide positive and negative feedbacks on front dynamics leading to accelerated and decelerated fronts, respectively. Under two constraints, there is an interplay between positive and negative feedback resulting in an oscillatory instability of a stationary front and large-amplitude limit-cycle motion. The instability occurs purely due to the global coupling and is not sensitive to the effect of the boundaries.