7. Systems with 2 different multipliers in both right parts, belonging to a B class

In this section, the full solution of our task for Eq. (3) systems of the B class is given:

Phase Portraits of Cubic Dynamic Systems in a Poincare Circle http://dx.doi.org/10.5772/intechopen.75527 77

$$\frac{d\mathbf{x}}{dt} = p(y - u\_1\mathbf{x})^2(y - u\_2\mathbf{x}),\\\frac{dy}{dt} = \mathbf{q}(y - q\_1\mathbf{x})(y - q\_2\mathbf{x}).\tag{5}$$

For an arbitrary Eq:ð Þ5 – system, P(u), Q(u) are the system's polynomials P, Q.

$$\mathbf{P}(\mathbf{u}) \colon= X(1,\boldsymbol{u}) \equiv p(\boldsymbol{u} - \boldsymbol{u}\_1)^2 (\boldsymbol{u} - \boldsymbol{u}\_2), \quad \mathbf{Q}(\boldsymbol{u}) \colon= Y(1,\boldsymbol{u}) \equiv q(\boldsymbol{u} - q\_1)(\boldsymbol{u} - q\_2),$$

RSPQ shows 6 different variants, because C<sup>2</sup> <sup>4</sup> ¼ 6.

We can thus conclude that all Eq. 5ð Þ family of systems is split into 52 different subfamilies, and all systems of each chosen subfamily show in a circle Ω, one common type of a phase portrait belonging to this particular subfamily. We have constructed all 52 topologically different phase portraits.
