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Analyze the stability of equilibrium point $\bar{x}=0$ of the system: (Does it have more than one equilibrium point?)

$\left\{ \begin{array}{lcc} \dot{x_1}=x_1(a-bx_2) \\ \\ \dot{x_2}=x_2(-c+dx_1) \end{array} \right.$

I tried this by using Bendixson criteria or a Liaponouv's function but I don't know how to approach this. Thanks for your help!

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  • $\begingroup$ @MrYouMath when $a, b, c, d >0$ this is a predator-prey model. $\endgroup$ – user425181 Nov 29 '17 at 20:29

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