On geometric structure of phase portraits of some piecewise linear dynamical systems

V. P. Golubyatnikov, L. S. Minushkina

We construct an invariant surface in a non-invariant domain of phase portrait of one piecewise linear dynamical system which appears naturally in gene networks modeling. This surface does not intersect the invariant neighborhood of a cycle which we have found in that phase portrait earlier, neither it contains other cycles of this system. All trajectories of this system contained in this surface are attracted to a point which plays role of an equilibrium point for smooth dynamical systems of this type. 

Tbilisi Mathematical Journal, Special Issue (7 - 2021), pp. 49-56