In this paper, we present a compact SPICE model of an analog switching memristive device based on niobium oxide and investigate the functionality of the same as a synapse element through its compact model by utilizing it in a simulation of an 8x8 resistive crossbar array. Considering especially the von Neumann bottleneck for neural network computing tasks, memristive crossbar arrays offer a potential in-memory computing solution performing highly parallel matrix-vector multiplication and reducing the energy consumption. In particular, multilevel switching memristive devices with intrinsic self-compliance are predestined for crossbar operations. Based on experimental results of a bi-layer Ti/Al2O3/Nb2O5/Ti stack, a compact physical model was recently derived, assuming an underlying PooleFrenkel emission mechanism. High model accuracy in terms of I-V behaviors, dynamic route map and power exponent plots were demonstrated by fitting the nonlinear I-V relation and the state function to measurement data, verifying analog gradual switching for the voltage driven extended memristor. In this paper the SPICE implementation for the core memductance accompanied by a parallel and series resistor is introduced and its application for sense analysis via analog and multi-memristor circuit exploitation is presented. Adopting the SPICE model, the switching dynamics is investigated and discussed for performing synaptic potentiation and depression behavior in a potential crossbar application.