consisting of critical points of the integral map. The idea of a critical subsystem is as follows [@KhRCD; @KhHMJ]. Let $$J=H{\times}K{\times}G: {\mathcal{P}}^6 \to {\mathbb{R}}^3$$ be the integral map of the system and let $\mathcal{C}$ be the set of its critical points. Obviously, $\mathcal{C}$ is stratified by ${\mathop {\rm rank}\nolimits}J$ and for $x\in \mathcal{C}$ the number ${\mathop {\rm rank}\nolimits}J(x)$ is called the rank of the critical point $x$. The set $J(\mathcal{C})$ is called the bifurcation diagram of $J$ and is also stratified by the maximal rank on the pre-images of its points. Smooth imensional surfaces or isolated imensional curves in $J(\mathcal{C})$ are called the leaves of the bifurcation diagram. Suppose that $$\label{eq2_10}
{\mathcal{L}}(h,k,g)=0$$ is the equation of a 2-surface $\Pi_{\mathcal{L}}\subset {\mathbb{R}}^3$ bearing one of the imensional leaves. Let $$\label{eq2_11}
\Phi_{\mathcal{L}}={\mathcal{L}}\circ J: {\mathcal{P}}^6 \to {\mathbb{R}}.$$ Then the critical subsystem $\mathcal{J}_{\mathcal{L}}$ (of rank 2) is the closure of the set of critical points of rank 2 belonging to the level $\Phi_{\mathcal{L}}=0$ (to the pre-image of $\Pi_{\mathcal{L}}$). Obviously, $\mathcal{J}_{\mathcal{L}}$ is an invariant subset in ${\mathcal{P}}^6$ consisting of critical points of $J$. Therefore, speaking of a critical subsystem we always have in mind the induced dynamics. The subset $\mathcal{J}_{\mathcal{L}}$ is almost everywhere a 4-dimensional manifold 