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$$\begin{array}{lcl}

\frac{du_1}{d\tau} & = & (1-u_1-a_{12}u_2)\\

\frac{du_2}{d\tau} & = & (1-u_2-a_{21}u_1)

\end{array}

$$

The steady states for this system are $(0,0)$, $(1,0)$, and $(0,1)$.

But then the book says without explanation

$\displaystyle u_1^* = \frac{1-a_{12}}{1-a_{12}a_{21}}$

and

$\displaystyle u_2^* = \frac{1-a_{21}}{1-a_{12}a_{21}}$

Never mind solve the problem

\frac{du_1}{d\tau} & = & (1-u_1-a_{12}u_2)\\

\frac{du_2}{d\tau} & = & (1-u_2-a_{21}u_1)

\end{array}

$$

The steady states for this system are $(0,0)$, $(1,0)$, and $(0,1)$.

But then the book says without explanation

$\displaystyle u_1^* = \frac{1-a_{12}}{1-a_{12}a_{21}}$

and

$\displaystyle u_2^* = \frac{1-a_{21}}{1-a_{12}a_{21}}$

Never mind solve the problem

Last edited: