On some nonlinear dynamical systems modelling asymmetric gene networks

We consider a wide class of 3-dimensional nonlinear dynamical systems as models of asymmetric gene networks functioning. The networks are being considered with negative feedbacks and with different regulation mechanisms. For these dynamical systems, geometric and topological characteristics of their phase portraits are studied, necessary and sufficient conditions of periodic trajectories existence are obtained, also Andronov–Hopf bifurcations are described.