In this work 3 x 3 crossbar arrays of titanium oxide were fabricated and tested for non-volatile memory applications and neuromorphic pattern recognition. The non-volatile memory characteristics of the memristor were examined using retention tests for each memristor. In order to test neuromorphic pattern recognition, the memristor crossbar array was programmed to store '111', '100' and '010' at the first, second and third columns of the array, where '0' and '1' represent the high-resistance state (HRS) and low-resistance state (LRS), respectively. The three similar input patterns of '111', '100' and '010' were applied to the crossbar array, for pattern recognition. Using a twin memristor crossbar array mechanism all three input patterns were recognized.