  In this paper, we study the stability of an Ordinary Differential Equation
(ODE) usually referred to as Cyclic Feedback Loop, which typically models a
biological network of molecules where each molecule regulates its successor in
a cycle. Regulations, which can be either positive or negative, are modelled by
increasing or decreasing functions. We make a complete analysis of this model
for a wide range of functions (including affine and Hill functions) by
determining the parameters for which bistability and oscillatory behaviours
arise. These results encompass previous theoretical studies of gene regulatory
networks, which are particular cases of this model.
