Logistic Function Based Memristor Model with Circuit Application

Abstract

A new SPICE compatible memristor model is presented which is based on the solution to the well-known Logistic equation. Previously published first order function models are limited in their ability to elucidate the memristor's oscillatory and chaotic behavior. Fractional order models are not SPICE friendly although they are known to demonstrate chaos. The relationship between the logistic equation and its iterated map is used to show how the proposed model explains the memristor's oscillatory and chaotic characteristic. It emulates empirically observed ohmic and semiconducting response to temperature. The utility of the model is tested by implementing it in a novel reliability and power aware relaxation oscillator design. A methodical approach to estimating the oscillation frequency of such highly nonlinear circuitry is presented. Computed results are validated against the relaxation oscillator implemented in an LTSpice testbench.