We obtain some sufficient conditions for the existence of a periodic trajectory of the Elowitz-Leibler type piecewise linear dynamical system that simulates a simplest nonsymmetric circular gene network. We prove the monotonicity of the corresponding Poincaré mapping and construct an invariant toric neighborhood of this cycle.
- circular gene network
- invariant domain
- piecewise-linear dynamical system
- Poincaré mapping
- positive and negative feedbacks