- #1

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[tex]\frac{du}{dt}=ru\left(1-\frac{u}{q}\right)-\left(1-\exp\left(-\frac{u^2}{\varepsilon}\right)\right)=0[/tex]

I have tried using Mathematica and Mathematica couldn't solve it.

I tried some algebra and that wasn't going anywhere so I am at a loss here.

Then in order to determine if the model has hysteresis, I have to make the substitution

[tex]r=\frac{R}{\sqrt{\varepsilon}}[/tex]

and

[tex]u=U\sqrt{\varepsilon}.[/tex]

And show that there is a nose at R=0.638.

After I make the substitutions, what do I do to show the nose at R=0.638?

Thanks.