Modeling and Dynamics Analysis of a Universal Interface for Constructing Floating Fractional Order Mem-Elements

Fractional-order systems generalize classical differential systems and have empirically shown to achieve fine-grain modeling of the temporal dynamics and frequency responses of certain real-world phenomena. Although the study of integer-order memory element (mem-element) emulators has persisted for several years, the study of fractional-order memory elements (FOMEs) has received little attention. To promote the study of the characteristics and applications of mem-element systems in fractional calculus (FC) and memory systems, in this paper, we propose a novel universal interface for constructing floating FOMEs. When the topological structure of the interface remains unchanged, the floating fractional-order memristor (FOMR), fractional-order memcapacitor (FOMC) and fractional-order meminductor (FOMI) emulators can be realized by using the impedance combinations of different passive elements, without any mem-element emulators and mutators. When compared with previously proposed FOMEs, the proposed fractional-order mem-element emulators based on a universal interface not only feature the characteristics of floating terminals and simpler circuit structures, but can also realize all three different types of FOMEs. To explore the dynamical relationships between the mem-elements and the fractional order, we mathematically derive and analyze the maximum and minimum possible values of memductance, memcapacitance and inverse meminductance which accounts for practical design considerations when building FO systems. The memory characteristics of FOMEs are analyzed by varying their orders and stimuli frequencies. The consistency of theoretical analysis, numerical calculation and simulation results validates the correctness of our proposed emulators.