On the stability of nonlocal oscillations in one piecewise-linear dynamical system

We study the structure of the phase portrait of a three-dimensional dynamical system simulating the functioning of a simple molecular repressilator. The existence of a unique asymptotically stable equilibrium point is proven. Conditions for the existence and stability of a closed trajectory lying in the complement to the domain of attraction of this point are obtained.

УДК 517.938

Ключевые слова: gene network models, dynamical systems, phase portraits, equilibrium points, periodic solutions, step functions, nonlocal oscillations.