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Consider the non linear system X dot = y + x(x^2 + y^2 - 1) *...

Consider the non linear system
X dot = y + x(x^2 + y^2 - 1) * sin 1 /x^2 + y^2 - 1
Y dot = - x + y(x^2 + y^2 - 1) * sin 1/ x^2 + y^2 - 1
Without solving the above equations explicitly, show that the system has infinite number of limits cycles. Determine the stability of these limit cycles (Hint : Use polar coordinates)

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