Consensus reaching in swarms ruled by a hybrid metric-topological distance

Recent empirical observations of three-dimensional bird flocks and human crowds have challenged the long-prevailing assumption that a metric interaction distance rules swarming behaviors. In some cases, individual agents are found to be engaged in local information exchanges with a fixed number of neighbors, i.e. a topological interaction. However, complex system dynamics based on pure metric or pure topological distances both face physical inconsistencies in low and high density situations. Here, we propose a hybrid metric-topological interaction distance overcoming these issues and enabling a real-life implementation in artificial robotic swarms. We use network- and graph-theoretic approaches combined with a dynamical model of locally interacting self-propelled particles to study the consensus reaching process for a swarm ruled by this hybrid interaction distance. Specifically, we establish exactly the probability of reaching consensus in the absence of noise. In addition, simulations of swarms of self-propelled particles are carried out to assess the influence of the hybrid distance and noise

Connecting Core Percolation and Controllability of Complex Networks

Core percolation is a fundamental structural transition in complex networks related to a wide range of important problems. Recent advances have provided us an analytical framework of core percolation in uncorrelated random networks with arbitrary degree distributions. Here we apply the tools in analysis of network controllability. We confirm analytically that the emergence of the bifurcation in control coincides with the formation of the core and the structure of the core determines the control mode of the network. We also derive the analytical expression related to the controllability robustness by extending the deduction in core percolation. These findings help us better understand the interesting interplay between the structural and dynamical properties of complex networks