engleski

The dynamics of some cubic vector fields with a center

We study planar cubic vector fields $$V_H=yP_2\frac{; ; \partial}; ; {; ; \partial x}; ; -xQ_2\frac{; ; \partial}; ; {; ; \partial y}; ; $$ with a center having Darboux first integral $H=P_1^2Q_3$. We give the bifurcation diagram of the phase portraits of the vector field, in 2-dimensional parameter space.

cubic vector field

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