Pinched hysteretic loops of ideal memristors, memcapacitors and meminductors must be ‘self-crossing’

Recently, novel findings have been published, according to which some mem-systems excited by harmonic signals can be characterised by the so-called ‘non-crossing-type pinched hysteretic loops’. Presented is a proof that this phenomenon cannot occur in ideal memristors, memcapacitors and meminductors which are defined axiomatically via the corresponding constitutive relations or via other equivalent characteristics, and that the ‘crossing-type hysteretic loop’ is thus one of their typical fingerprints.