In this paper¹ a stability analysis sheds light into aspects of memristor circuit design, revealing a circuit theoretic technique for the stabilization of the NDR portion of the device DC characteristic. This type of studies supports the work of designers exploring memristor potential in electronics. Concepts from nonlinear dynamics theory allow us to gain a deep understanding of the dynamics of our locally-active memristor. The analysis provides hints on how to design an oscillator where limit-cycle behavior emerges from the locally-active threshold switching of the memristor, as theoretically proved here.