Control energy of complex networks towards distinct mixture states

Sen Nie,H Eugene Stanley,Xu-Wen Wang,Shi-Ming Chen,Bing-Hong Wang

doi:10.1038/s41598-018-29207-x

Sen Nie, H Eugene Stanley + Show 3 more

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https://doi.org/10.1038/s41598-018-29207-x

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Controlling complex networked systems is a real-world puzzle that remains largely unsolved. Despite recent progress in understanding the structural characteristics of network control energy, target state and system dynamics have not been explored. We examine how varying the final state mixture affects the control energy of canonical and conformity-incorporated dynamical systems. We find that the control energy required to drive a network to an identical final state is lower than that required to arrive a non-identical final state. We also demonstrate that it is easier to achieve full control in a conformity-based dynamical network. Finally we determine the optimal control strategy in terms of the network hierarchical structure. Our work offers a realistic understanding of the control energy within the final state mixture and sheds light on controlling complex systems.

Highlights

Because it can accurately characterize such real-world systems as social networks[1,2,3], biological networks[4,5,6,7], technical networks[8,9], and financial networks[10,11,12,13], network science has been a popular research topic for decades
Since conformity behavior-based dynamics facilitates the controllability of an identical state[39], we examine the control energy of such a conformity-based dynamical network
There is a longer distance between the identical final state and its initial state, the control energy is less than that required to reach a non-identical final state

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Introduction

Because it can accurately characterize such real-world systems as social networks[1,2,3], biological networks[4,5,6,7], technical networks[8,9], and financial networks[10,11,12,13], network science has been a popular research topic for decades. We explore the control energy by examining the number of driver nodes needed to direct the system from an initial state to either an identical or non-identical final state. Inset: Control energy as a function of average degrees k in directing the random network to the identical final state (c = 3).

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