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In this paper, we study the pulsating traveling fronts for a spatially discrete periodic reaction–diffusion system with a quiescent stage. It is known that there exists a critical number c∗ > 0 (called minimal wave speed) such that a pulsating traveling front exists if and only if its speed is above c∗. In this paper, we derive a uniqueness theorem for supercritical pulsating traveling fronts. Further, we show that all supercritical pulsating traveling fronts are exponentially stable. [ABSTRACT FROM AUTHOR]