- #1
fauboca
- 158
- 0
I am trying to show that there are 3 nonzero steady states of
[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.
[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.