Phase portraits of multiply connected n-dimensional state-spaces

Question

I ask for help in my attempts to understand the following question.

There is an n-dimensional nonlinear state-space of the following form:

$\begin{cases} \dot{x} = (x^2 + y^2 + z^2)*sin(t) - sin(t+\pi/2) \\ \dot{y} = (x^2 + y^2 + z^2)*1.1sin(2t) - 1.1sin(2t+\pi/2) \\ \dot{z} = (x^2 + y^2 + z^2)*1.2sin(3t) - 1.3sin(3t+\pi/2) \end{cases}$

There is a rule according to which the dynamic features of the system can be estimated by constructing the C (n, 2) phase planes of combinations of variables of the state space.

${C_{{2}}}^{n}=1/2\,{\frac {n}{ \left( n-2 \right) !}}$

In the article On the n-Dimensional Phase Portraits state-space is divided into pairs of equations that are combinations of different variable states, and phase planes are constructed for these combinations. What if several state variables are included in these pairs of states? For example, a paired combination of state-space variables would be the following equation:

$\begin{cases} \dot{x} = (x^2 + y^2 + z^2)*sin(t) - sin(t+\pi/2) \\ \dot{y} = (x^2 + y^2 + z^2)*1.1sin(2t) - 1.1sin(2t+\pi/2) \end{cases}$

For me, this is like solving a system of two equations with the number of variables greater than 2.

I realized that first need to deal with the mathematical side of the issue.

1. How build phase portraits for an n-dimensional state space if it is non-autonomous (time-varying sinusoidal signals are included in the system)?
2. Is it possible to solve the problem by evaluating the closedness of a 1-form and determining the linear dependence / independence of 1-forms for the corresponding pair of Pfaff equations?

I assume that the expression

$x^2 + y^2 + z^2$

can be divided into sums of variables and write pairs of equations in the following form and investigate them already, for example, introducing, therefore, new state variables.

$\begin{cases} \dot{X} = (x^2 + y^2)*sin(t) - sin(t+\pi/2) \\ \dot{Y} = (x^2 + y^2)*1.1sin(2t) - 1.1sin(2t+\pi/2) \end{cases}$

$\begin{cases} \dot{Y} = (y^2 + z^2)*1.1sin(2t) - 1.1sin(2t+\pi/2) \\ \dot{Z} = (y^2 + z^2)*1.2sin(3t) - 1.2sin(3t+\pi/2) \end{cases}$

Are my arguments true?