We obtain conditions for uniqueness of a cycle in the phase portraitof a piecewise linear dynamical systemof the Elowitz–Leibler typewhich simulates the functioning of a simplest circular gene network.We describe the behavior of trajectories of this systemin the invariant toric neighborhood of the cycle.
- block-linear dynamical system
- circular gene network
- fixed point
- invariant domain
- Poincaré map
- positive and negative feedbacks
- 1.01 MATHEMATICS