Controllability of Complex Networks with Nonlinear Dynamics

Department of Physics and Centre for Computational Science and Engineering,National University of Singapore, Singapore 117546, Republic of Singapore(Dated: July 13, 2011)The controllability of large linear network systems has been addressed recently [Liu et al. Nature (London),473, 167 (2011)]. We investigate the controllability of complex-network systems with nonlinear dynamics byintroducing and exploiting the concept of “local effective network” (LEN). We find that the minimum numberof driver nodes to achieve full control of the system is determined by the structural properties of the LENs.Strikingly, nonlinear dynamics can significantly enhance t he network controllability as compared with lineardynamics. Interestingly, for one-dimensional nonlinear nodal dynamics, any bidirectional network system canbe fully controlled by a single driver node, regardless of the network topology. Our results imply that real-worldnetworks may be more controllable than predicted for linear network systems, due to the ubiquity of nonlineardynamics in nature.

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