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[SOLVED] Budworm Model


Well-known member
Feb 1, 2012
dimensionless ODE


$\displaystyle U=r-\frac{ru}{q}$ and $\displaystyle V=\frac{u}{1+u^2}$

Show using conditions of a double root that the steady state is given parametrically by

$\displaystyle r=\frac{2a^3}{(1+a^2)^2}$, $\displaystyle q=\frac{2a^3}{a^2-1}$

$\displaystyle U'=-\frac{r}{q} = \frac{1-u^2}{(1+u^2)^2}=V'$

Solving for r

$\displaystyle r=\frac{(u^2-1)q}{(1+u^2)^2}$

Now substitution


If I solve for q, I will have a quadratic. Is there a mistake or something I am not seeing?

---------- Post added at 01:27 PM ---------- Previous post was at 12:06 PM ----------

I solved via Mathematica. Everything was correct.