Are the dynamics on slide 10 correct?

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The dynamics equations on slide 10 of Lecture 3-1 do not correspond to the plots of the time response and the phase portrait. The correct dynamics equations are

d(x_1)/dt = -x_2 - x_1*(1-x_1^2 - x_2^2),

d(x_2)/dt = x_1 - x_2*(1-x_1^2 - x_2^2).