This paper proposes the derivation of a physics-based model of an analog memristive device realized as a bi-layer Al₂O₃/Nb₂O₅ stack. Memristive crossbar arrays implementing matrix-vector multiplications are a central building block of novel computing-in-memory architectures for artificial neural network and neuromorphic computing applications. The presented memristor shows analog, multi-level switching at high resistances without electroforming and is suitable for crossbar operations with low energy consumption. By including a graphical analysis method of the I-V curves obtained in a quasi-static approach, the dynamic behavior is analyzed with regard to ohmic and Poole-Frenkel behavior. Finally, a compact model, represented by an algebraic differential equation, is proposed and verified by fitting calculated solutions to experimental data.