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Question about memristor and memristive system

Hi, i'm not able to relate a memristor and a memristive system. I consider a memristive system:

dx/dt=f(x,u,t) y=g(x,u,t)u

where x=state u=input y=output t=time

and a memristor:

dfi/dq=M v=Mi

where fi=flux q=charge M=memresistance i=current v=voltage

a memristor is a special case of a memristive system where:

  1. x=q
  2. u=i
  3. y=v
  4. consider a time invariant model How can i connect dx/dt=f(x,u,t) with dfi/dq=M? dq/dt=(1/M)dfi/dt, so f(x,u)=(1/M)dfi/dt? If so, f(x,u) has not a direct relation with charge (x) and current (i), or not? Thanks
Reply to
eryer
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You can start by reading the Wikipedia page on memristors, where you will find your equations in error, by leaving out the dependence of M on q. You will also find your answer, nearly complete and ready for you to copy down.

If you use Wikipedia's equation

dfi/dt v(t) M(q(t)) = ------ = ---- dq/dt i(t)

then you can take q as your state variable:

dq/dt = i

and

v(t) = M(q(t)) * i(t)

Or, to fit this into the general system that you are proposing,

f(q, i, t) = i

and

g(q, i, t) = M(q(t))

So, there you have it: one time-invariant, albeit nonlinear, equation.

--
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com
Reply to
Tim Wescott

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