EXERCISE 1. For the following ODE system find ALL its equilibrium points and find their stability using the Jacobian.\\ $\begin{cases} x' = x(x + y - 3), \\ y' = y(2x + y - 4). \end{cases}$
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For x', we have x(x + y - 3) = 0. This equation is satisfied when x = 0 or x + y - 3 = 0. For y, we have y(2x + y - 4) = 0. This equation is satisfied when y = 0 or 2x + y - 4 = 0. So the equilibrium points are: Show more…
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