Conditions for realization of multiple pinch‐off points in generalized fractional‐order memory elements

Summary Memelements (memristor, meminductor, and memcapacitor) have gained wide interests due to their useful hysteresis and nonlinear properties. In this work, fractional‐order current‐controlled memelements are modeled using an ‐order polynomial. By decomposing the ‐order polynomial into some sets of current‐controlled functions, we were able to theoretically analyze and establish the general conditions necessary for all memelements' voltage‐current dynamics to create up to number of lobes and hence pinch‐off points in their hysteresis. The exact coordinate locations of the pinch‐off points on the ‐axis and ‐axis are calculated in all cases. The observations made in this work are novel and contributes to how all multiple‐lobed memory elements are analyzed. A general emulator circuit is then designed to verify the theoretical deductions, the emulator output agrees with the numerical results.