This work aims to demonstrate the utilization of fabricated memristors in bioinspired analog circuits. To this end, two types of memristors of the structures Pt/TiO2/TiOx/Pt and Au/TiO2/TiOx/Au have been fabricated and characterized. The current-voltage measurement results were used to derive models for these devices both through curve fitting using MATLAB and consulting models proposed by other groups. A Verilog-A model was developed for modelling our fabricated memristor, which was used in Cadence Spectre simulations of an analog weak inversion Half Center Oscillator (HCO) circuit. The simulations show, through comparison of HCOs employing our memristors, linear resistors and no memristors or resistors, that the varying resistance of memristors create a dynamic damping effect and result in the modification of oscillation amplitude, rhythm and improved cycle stability.