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**seadog** "$\displaystyle x_1' = x_1 -\alpha x_2$

$\displaystyle x_2' = \beta (x_1 - x_2 - G)$

$\displaystyle

1< \alpha < \infty, 1 \leq \beta < \infty

$

a) Show that if $\displaystyle G = G_0$ is constant, there is an equilibrium state. Classify the equilibrium state and show that the system oscillates when $\displaystyle \beta$ = 1.

b) Suppose $\displaystyle G=G_0+kx_1$ where k>0. Show that there is no equilibrium state if $\displaystyle k \geq (\alpha -1)/\alpha$. How does the system behave?

c) Show there are two equilibrium states if $\displaystyle G=G_0+kx_1^2$. Characterize the equilibrium points."

I'm pretty confused by how my professor worded this problem. Can someone just clarify or paraphrase what it's asking for? I'm particulary wondering what he meant by "Classify the equilibrium state..." in part a and "Characterize the equilibrium points..." in part c.