Impulsive control of a nonlinear dynamical network and its application to biological networks

The control of nonlinear dynamical systems is always a notable problem in science. According to control theory, suitable inputs for a controllable dynamical system are critical. Previous studies have shown some principles to determine control nodes and design control function. In this work, we propose a new control strategy of nonlinear systems by constructing impulsive control functions, i.e., we can realize the transition from an undesired state to a desired one by controlling appropriately chosen nodes in a discrete manner. In order to demonstrate the effectiveness of the strategy, we apply it to two biological networks: the epithelial–mesenchymal transition (EMT) network and the Notch1–Dll1–Jag1 signaling pathway. The strategy can not only be used to guide pharmacological design in a more feasible form but can also be applied into the fields of biological, medical and other multistable dynamical systems.