The resistive switching and synaptic behavior of a fabricated Ti/HfO2/Pt crossbar array device are investigated. The results demonstrated that TiOx layers are created by the movement of oxygen ions during the positive SET process, thereby improving the endurance and multilevel switching behavior of the device. The random properties of SET process were described with the help of stochastic model of memristor based on the length of conductive filament. The analysis of the mean first passage time allows estimating the parameters of the dielectric switching layer such as the activation energy of the diffusive defects, its variation under the influence of the driving voltage and the value of the working temperature. Furthermore, the conductive mechanism of the Ti/HfO2/Pt device with temperature variations and Schottky emission fitting was studied. Furthermore, the potentiation, depression, and the spike-time dependent plasticity behavior of the Ti/HfO2/Pt devices have been demonstrated by well-designed pulse inputs. The observed gradual change in conductance is suitable for a synaptic device in a neuromorphic system. o̧pyright 2022 Elsevier Ltd