\[
\boxed{
 \left\{ {\frac {\rm d}{{\rm d}t}}x \left( t \right) =x \left( t \right) +y \left( t \right) -x \left( t \right)  \left(  \left( x \left( t \right)  \right) ^{2}+ \left( y \left( t \right)  \right) ^{2} \right) ,{\frac {\rm d}{{\rm d}t}}y \left( t \right) =-x \left( t \right) +y \left( t \right) -y \left( t \right)  \left(  \left( x \left( t \right)  \right) ^{2}+ \left( y \left( t \right)  \right) ^{2} \right)  \right\} }
\]