Abstract
Despite the significant advances in identifying the driver nodes and energy requiring in network control, a framework that incorporates more complicated dynamics remains challenging. Here, we consider the conformity behavior into network control, showing that the control of undirected networked systems with conformity will become easier as long as the number of external inputs beyond a critical point. We find that this critical point is fundamentally determined by the network connectivity. In particular, we investigate the nodal structural characteristic in network control and propose optimal control strategy to reduce the energy requiring in controlling networked systems with conformity behavior. We examine those findings in various synthetic and real networks, confirming that they are prevailing in describing the control energy of networked systems. Our results advance the understanding of network control in practical applications.
Highlights
Network has been a powerful structure representation of social [1–5], economic [6, 7], biological [8–10] and transportation systems [11–13]
Recent advances in control mode [18–22], optimal driver nodes set [23–25] and control of nonlinear dynamic systems [26, 27] have offered important insights in understanding the controllability of complex networked systems. Energy requiring is another key characteristic when control a network in practice, which is simultaneously determined by Optimal control of complex networks with conformity behavior controllability Gramian matrix, control time, initial state and final state [28–32]
We explore the influence of conformity behavior on control energy for both synthetic and real networks
Summary
Network has been a powerful structure representation of social [1–5], economic [6, 7], biological [8–10] and transportation systems [11–13]. Energy requiring is another key characteristic when control a network in practice, which is simultaneously determined by Optimal control of complex networks with conformity behavior controllability Gramian matrix, control time, initial state and final state [28–32]. Wang et al [48] introduced the conformity into network control and found that the dynamical networked system with conformity behavior tends to require less number of driver nodes.
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