title: Intrinsic dynamics induce global symmetry in network controllability.
abstract: Controlling complex networked systems to desired states is a key research goal in contemporary science. Despite recent advances in studying the impact of network topology on controllability, a comprehensive understanding of the synergistic effect of network topology and individual dynamics on controllability is still lacking. Here we offer a theoretical study with particular interest in the diversity of dynamic units characterized by different types of individual dynamics. Interestingly, we find a global symmetry accounting for the invariance of controllability with respect to exchanging the densities of any two different types of dynamic units, irrespective of the network topology. The highest controllability arises at the global symmetry point, at which different types of dynamic units are of the same density. The lowest controllability occurs when all self-loops are either completely absent or present with identical weights. These findings further improve our understanding of network controllability and have implications for devising the optimal control of complex networked systems in a wide range of fields.
authors: School of Systems Science, Beijing Normal University, Beijing, 10085, P. R. China.
authors: Chen
authors: C
authors: Zhao
authors: School of Systems Science, Beijing Normal University, Beijing, 10085, P. R. China.
authors: Wen-Xu
authors: WX
authors: Wang
authors: 1] Channing Division of Network Medicine, Brigham and Women's Hospital, Harvard Medical School, Boston, Massachusetts 02115, USA [2] Center for Complex Network Research and Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA.
authors: Yang-Yu
authors: YY
authors: Liu
authors: 1] Nonlinear Systems Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139, USA [2] Department of Mechanical Engineering and Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139, USA.
authors: Jean-Jacques
authors: JJ
authors: Slotine