This work presents a mathematical analysis of HP's memristor models, a skeleton integrator circuit which utilises a memristor, a CMOS-based weak inversion memristor dynamics emulator and a CMOS implementation of a neural network which employs memristors. The implications of the nonlinear dynamics of the memristor and its property of integrating its input are studied. By using an adjustable piecewise input signal, memristance is studied for various excitation signals for current driven and voltage driven memristor models. The importance of the timing, the amplitude and DC offset of the input signal and the resulting mean value with regards to how memristance variation is affected is investigated. A symbolic analysis of a simple memristor-capacitor circuit is carried out inspired by the simplest neuron model of a resistor-capacitor circuit.


Having understood the dynamics exhibited by HP's memristor, the integration property of the device is exploited to attain a memristor-based, low power, capacitor-less, CMOS integrator circuit operating in weak inversion. Simulation results showing frequency and transient responses of the circuit are presented. The implications of varying memristor characteristics upon the operation of the integrator are investigated. Inspired by the natural nonlinear dynamics exhibited by CMOS devices operating in weak inversion, a compact, nanopower memristor dynamics integrator is presented. The memristive output of this emulator can be related to a charge-driven prototype memristor with a flux exponentially related to its charge. The memristor is also introduced to a CMOS implementation of a neural network known as a central pattern generator. The effect of including memristors in different configurations upon the nonlinear biological dynamics exhibited by this circuit is observed. The variation in the oscillation amplitude, rhythm and the added stability due to the memristors are reported. This work is a study of memristive dynamics and proposes various applications of this component which governs integration capabilities and can offer power efficient operation and low area consumption in analogue circuits.