Research paperBistability and delay-induced stability switches in a cancer network with the regulation of microRNA

•Dynamics of a cancer network with the regulation of microRNA is investigated.•The existence of multiple steady states, bistability and dependency on the parameters are obtained.•Both stabilizing and destabilizing role of time delay are thoroughly analyzed.

In this paper, we are concerned with a cancer network including a protein module and a corresponding microRNA cluster that inhibits the synthesis of proteins. The existence of multiple steady states and their stability depending on the parameters are firstly determined. Bistability and dependency on the parameters, Hopf bifurcations and the corresponding properties like direction and stability of Hopf bifurcations are determined by computing the normal form on the center manifold. Then, the role of the delay in the process of synthesis of the protein is investigated. We show that the delay can stabilize the unstable equilibrium and destabilize the stable equilibrium. Some simulations are carried out to numerically illustrate the obtained theoretical results. Finally, the biological interpretation of the theoretical results is discussed.