Heteroclinic cycles in the repressilator model

A repressilator is a synthetic regulatory network that produces self-sustained oscillations. We analyze the evolution of the oscillatory solution in the repressilator model. We have established a connection between the evolution of the oscillatory solution and formation of a heteroclinic cycle at infinity. The convergence of the limit cycle to the heteroclinic cycle occurs very differently compared to the well-studied cases. The transition studied here presents a new bifurcation scenario.

► We conduct analysis at infinity in the phase space of the repressilator model. ► We study two models with the original linear and a new saturable degradation terms. ► We link the evolution of an oscillatory solution with a heteroclinic cycle. ► The transition studied here presents a new bifurcation scenario.