Controlling a complex dynamical network to attain an inhomogeneous equilibrium

Many networks are made up of a few groups, with nodes in the same group having the same kind of function. In this work, the problem of controlling a complex dynamical network to attain an inhomogeneous equilibrium point is investigated, which means that nodes in the same group achieve the same equilibrium point as an isolated node, while different groups correspond to different equilibrium points. An open-loop constant control approach is first proposed to obtain the inhomogeneous equilibrium point of the network. Then, the feedback pinning control approach is applied to make the inhomogeneous equilibrium point asymptotically stable.