Fractional Circuit Elements: memristors, memcapacitors, meminductors and beyond

摘要

Memristor was postulated by Chua in 1971 by analyzing mathematical relations between pairs of fundamental circuit variables and realized by HP laboratory in 2008. This relation can be generalized to include any class of two-terminal devices whose properties depend on the state and history of the system. These are called memristive systems, including current-voltage for the memristor, charge-voltage for the memcapacitor, and current-flux for the meminductor. This paper further enlarge the family of elementary circuit elements, in order to model many irregular and exotic nondifferentiable phenomena which are common and dominant to the nonlinear dynamics of many biological, molecular and nanodevices.