Every Nonlinear Element from Chua's Table Can Generate Pinched Hysteresis Loops: Generalised Homothety Theorem

Abstract

The pinched hysteresis loops drawn in the voltage-current, voltage-charge, and flux-current characteristics belong to well-known fingerprints of the memory elements known as the memristor, memcapacitor, and meminductor. It is shown that generating such loops is in fact a natural attribute of all nonlinear elements from Chua's table, and that the hysteresis need not necessarily be a manifestation of the internal memory of the element. A generalized homothety theorem is introduced, which describes the regularities of such a hysteresis and its frequency dependence.

The pinched hysteresis loops drawn in the voltage-current, voltage-charge, and flux-current characteristics belong to well-known fingerprints of the memory elements known as the memristor, memcapacitor, and meminductor. It is shown that generating such loops is in fact a natural attribute of all nonlinear elements from Chua's table, and that the hysteresis need not necessarily be a manifestation of the internal memory of the element. A generalized homothety theorem is introduced, which describes the regularities of such a hysteresis and its frequency dependence.