Analysis of the nonlinear relations of generalized current-controlled fractional order memory elements

A generalized fractional order memory element model is established in this work. From the model, the time-domain voltage, flux and energy relations of three current-controlled fractional order memory elements (Memristor, Memcapacitor and Meminductor) are established. To better characterize how excitation current affects the nonlinear behaviors of current-controlled memory elements, quantities called Current-Control Parameters are defined from the model. These parameters are used to quantify the voltage-current and flux-current profiles of the generalized model and they are used to establish necessary conditions for its voltage-current or flux-current profile to transition from purely elliptical to single and double-loop shapes. It shows that defining memory elements by their current-control parameters is a better way to study their nonlinear dynamics. The findings of this work are verified by numerical simulations.