3. Does the system x ‘ = x – x ( x 2 + y 2 ) y ‘ = x – y ( x 2 + y 2 ) have a periodic solution…

3.          Does the system

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3. Does the system x ‘ = x – x ( x 2 + y 2 ) y ‘ = x – y ( x 2 + y 2 ) have a periodic solution…
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x' = x x(x2  + y2)

y' = x y(x2 + y2)

 

have a periodic solution on the unit circle?