Pinning a complex dynamical network to its equilibrium

By Xiang Li, Xiao Fan Wang, Guanrong Chen. IEEE Trans. Circuits Syst. I Regul. Pap., 2004

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Distributed adaptive control for synchronization of unknown nonlinear networked systems (2010, background): “The local neighborhood synchronization error for node i is defined as (Khoo et al., 2009; Li et al., 2004) ei = − j∈Ni aij xj − xi + bi (x0 − xi) (4) with pinning gains bi ≥ 0, and bi > 0 for at least one i.”
Control Principles of Complex Networks (2015, background): “…been extensively applied to the synchronization of coupled oscillators and flocking of interacting agents (Bernardo and DeLellis, 2014; Chen and Duan, 2008; Li et al., 2004; Porfiri and di Bernardo, 2008; Sorrentino et al., 2007a; Wang and Chen, 2002a,b; Yu et al., 2009a, 2013; Zou and Chen, 2008).”
Consensus of second‐order multi‐agent systems with exogenous disturbances (2011, background): “Since it is much more effective to pin some most highly connected nodes than some common nodes in a large-scale network [26, 27], we choose two nodes with high degrees pinned.”