[![enter image description here][1]][1]

That physically means you do not have a memristor which have passive magnetic properties that are symmetrical in polarity. That is until a threshold voltage then they conduct heavily and behave like linear resistance until the polarity is sufficient reversed. This creates a pulsed current with a linear R on voltage modulation until 0V then high impedance again on negative polarities.

The dynamic range of resistance depends on the physical properties of the doped region in length and width in nm.  the area of the curve maximizes memory from hysteresis whereas a resistor has no VI loop area. 

[So excessive voltage will cause the spike property.][2] Seen below with excess voltage.
[![enter image description here][3]][3]

Yet a capacitor and a diode have this similar property or a diode partially blown by ESD with lower R and higher C from the small gap.  LEDs have this property when wounded by ESD but still work.  


Adding DC bias does not simulate your hypothetical question as the amount of heavy conduction and nonlinear spike current requires a certain percentage of negative bias to regain the positive VI memory loop.  

V = X axis , I = Y axis vertical.

[![enter image description here][4]][4]


  [1]: https://i.sstatic.net/i3vxs.png
  [2]: http://www.falstad.com/circuit/circuitjs.html?ctz=CQAgjCCsCmC0AcICcA6A7PAzEp8AskmAbPAExiYhqnhQAMUcYYAUAOYiakOZ16fcBDYSwC2Q8EhpcefEAzB0GkJcPBxEYJg1h0UqinVLwlJUpjRpsmTCwBKEsFMdE1EE0pA01eyCwD2tET8DHh0OF4okPL6pNEMNBC2gRDBXiBhEZBggnqqRnh4YGFEcbQQ2dwBQSEZYESUpFExRtE0iZwsQA
  [3]: https://i.sstatic.net/dSJV4.png
  [4]: https://i.sstatic.net/weBkW.png