Structure of the phase portrait of a piecewise-linear dynamical system

We consider some piecewise linear $4$-dimensional dynamical system that models a gene network regulated by one negative feedback and three positive feedbacks. Glass and Pasternack described the conditions for the existence of a stable cycle in this model. We construct an invariant piecewise linear surface with nontrivial link with the Glass–Pasternack cycle outside the attraction domain of this stable cycle in the phase portrait of this system.