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.