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[SOLVED] Steady States

dwsmith

Well-known member
Feb 1, 2012
1,673
Steady states for a system of nondimensionalized DEs

$$
\begin{array}{lcl}
\frac{du_1}{d\tau} & = & u_1(1 - u_1 - a_{12}u_2)\\
\frac{du_2}{d\tau} & = & \rho u_2(a - a_{21}u_1)
\end{array}
$$

So $(0,0)$ and $(1,0)$. Are there any more? If so, how did you find them?
 

Jester

Well-known member
MHB Math Helper
Jan 26, 2012
183
What if

$1−u_1 −a_{12} u_2 = 0$ and $a−a_{21} u_1 = 0$?
 

dwsmith

Well-known member
Feb 1, 2012
1,673