9. Systems containing 2 and 1 different multipliers in right parts

In this section, we give the full solution of the problem for Eq. (7) systems, i.e., for the Eq. (1) systems of the kind

$$
\dot{\mathbf{x}} = p\_0 \mathbf{x}^3 + p\_1 \mathbf{x}^2 \mathbf{y} + p\_2 \mathbf{x} \mathbf{y}^2 + p\_3 \mathbf{y}^3 \equiv p\_3 (\mathbf{y} - \boldsymbol{\mu}\_1 \mathbf{x})^2 (\mathbf{y} - \boldsymbol{\mu}\_2 \mathbf{x})\tag{7}
$$

$$
\dot{\mathbf{y}} = \mathbf{x}^2 + b \mathbf{x} \mathbf{y} + c \mathbf{y}^2 \equiv c(\mathbf{y} - q\mathbf{x})^2,
$$

where p<sup>3</sup> > 0, c > 0, u<sup>1</sup> < u2, q ð Þ ∈R 6¼ u1, 2.

The process of study of these systems is quite similar to that previously described for other families of Eq. (1) systems. For an arbitrary Eq. (7) system, P(u), Q(u) are the system's polynomials P, Q:

$$P(\mu) \colon= X(1,\mu) \equiv p\_3(\mu - \mu\_1)^2(\mu - \mu\_2), \qquad Q(\mu) \colon= Y(1,\mu) \equiv c(\mu - q)^2,$$

and there exists 3 different variants for their RSPQs.

A conclusion from our research for this particular type of systems is the following.

We`ve revealed, that for every possible family of Eq. (7) systems, 7 different topological types of their phase portraits are being implemented. This means that for all three existing families of such systems, r = 1, 3, the number of different phase portraits is 21 [8, 9].
