Computing the number of limit circles



Is it a analytically method (not a graphically one) use to compute the number and the stability of the limit circles of the system of nonlinear equations dx/dt=g(x,y) and dy/dt=f(x,y)? Can I extract any information from the equilibrium equation, resulted from the two isoclines of the system, in order to solve the previous question?

Thank you,
Dragos Calitoiu
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