Transfer function of a memristor

[exp]

I am confused: An inductor can be described with one single parameter L and its transfer function is v(s)=s L i(s), similarly for a capacitance v(s)=1/(s C)*i(s)

However, for a memristor v(t)=M i(t), implying that the memristor itself is the transfer function! But this would imply that it can't be described with a single parameter M as in L or C.

Just to make sure: A memristor is not just a frequency dependent capacitance, right (s*R) ?

If it can be described with a single parameter M, this implies that it is either non-linear and/or a time-varying system which does not sound reasonable to me, given it is deemed the "fourth fundamental element".

Interestingly I seem to be the first person in the world asking this question ...

 

[D.A.(Tony)Stewart]

Its a resistor with hysteresis (memory)

 

[exp]

So what type of a system is a hysteresis (except a hard hysteresis which is clearly non-linear)?

Linear but time-variant?

Does this mean that there is no transfer function for a memristor?