Accurate modeling of locally active dynamics plays a critical role in memristor based neuromorphic circuit design. This paper introduces a physically meaningful locally active device model which is suitable for modeling locally active memristors or threshold switching devices. The proposed model is derived through a 2-transistor-1-resistor (2T1R) circuit which is originally composed of 2 BJTs and a linear bias resistor and is exhibiting negative differential resistance characteristics. To obtain a robust mathematical description with minimal complexity, we introduce an external capacitor into the 2T1R circuit such that it physically governs the respective dynamics. Adopting the Ebers-Moll model for the BJTs and utilizing the external capacitor voltage as the state variable, we precisely derive the differential algebraic set of equations for the 2T1R circuit. The numerical simulation results of the proposed model match very well with the Spice simulation results of the 2T1R circuit. The value of the external capacitor can be further tuned to dominate internal parasitics and control the switching speed of the 2T1R circuit accurately, which is an essential requirement in the design of neuromorphic circuits.