Consider the two$-$dimensional autonomous system

x$$y$=$x$(1$x$$y$)=$y$(34$y$12$x$)$x$=$x$(1$x$$y$)$y$=$y$(34$y$12$x$)$

$($a$)$ The critical points of the system above have the form

x$0=[00],$x$1=[0$y$1],$x$2=[$x$20],$x$3=[$x$3$y$3].$x$0=[00],$x$1=[0$y$1],$x$2=[$x$20],$x$3=[$x$3$y$3].$

Find these components.

y$1=$y$1=$

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x$2=$x$2=$

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x$3=$x$3=$

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y$3=$y$3=$

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