This movie demonstrates vividly the essence of the network controllability paper: How to control a complex network with minimum number of nodes? For a given directed network, we calculate its maximum matching: a largest set of edges without common heads or tails. From it we identify the minimum set of driver nodes to control. By injecting signals to those driver nodes, we can fully control the network. There is a "cactus" structure underlying the controlled network, which is the "skeleton" for maintaining controllability. We show the cactus structures for both random networks and real-world networks in the movie.
Une catastrophe, au sens mathématique, est une rupture de l'équilibre d'un système, afin de maintenir son équilibre. La singularité peut être vue comme une 'catastrophe' à venir de notre société, afin d'accéder à un nouvel équilibre, faisant émerger probablement une intelligence en réseau, une open-society, radicalement bottom-up (ou, comme toute catastrophe : son contraire... une société hiérarchisée et totalitaire, pour le bien et l'équilibre de chacun...). Quel avenir préparons nous, pour aborder ce changement de phase ?
I. Leyva, R. Sevilla-Escoboza, J. M. Buldú, I. Sendiña-Nadal, J. Gómez-Gardeñes, A. Arenas, Y. Moreno, S. Gómez, R.Jaimes-Reátegui, S. Boccaletti
Critical phenomena in complex networks, and the emergence of dynamical abrupt transitions in the macroscopic state of the system are currently a subject of the outmost interest. We report evidence of an explosive phase synchronization in networks of chaotic units. Namely, by means of both extensive simulations of networks made up of chaotic units, and validation with an experiment of electronic circuits in a star configuration, we demonstrate the existence of a first order transition towards synchronization of the phases of the networked units. Our findings constitute the first prove of this kind of synchronization in practice, thus opening the path to its use in real-world applications.
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