Bifurcations in simple genetic cyclic models

In order to describe genetic regulatory networks several deterministic models based on systems of nonlinear ordinary differential equations (ODEs) have been proposed. The Elowitz repressilator, modeled as a system of three genes that repress each other in a ring, is one of the most outstanding examples. Furthermore, systems that can display a coexistence of different stable attractors are widely exploited in systems biology in order to suitably model the differentiating processes arising in living cells. The aim of the manuscript is to investigate the global periodic oscillations and their bifurcations in networks composed of simple bio-inspired oscillators that have a stable limit cycle and equilibrium point, separated by an unstable limit cycle.