3,286 research outputs found
Synchronization in complex networks
Synchronization processes in populations of locally interacting elements are
in the focus of intense research in physical, biological, chemical,
technological and social systems. The many efforts devoted to understand
synchronization phenomena in natural systems take now advantage of the recent
theory of complex networks. In this review, we report the advances in the
comprehension of synchronization phenomena when oscillating elements are
constrained to interact in a complex network topology. We also overview the new
emergent features coming out from the interplay between the structure and the
function of the underlying pattern of connections. Extensive numerical work as
well as analytical approaches to the problem are presented. Finally, we review
several applications of synchronization in complex networks to different
disciplines: biological systems and neuroscience, engineering and computer
science, and economy and social sciences.Comment: Final version published in Physics Reports. More information
available at http://synchronets.googlepages.com
Resilience and Controllability of Dynamic Collective Behaviors
The network paradigm is used to gain insight into the structural root causes
of the resilience of consensus in dynamic collective behaviors, and to analyze
the controllability of the swarm dynamics. Here we devise the dynamic signaling
network which is the information transfer channel underpinning the swarm
dynamics of the directed interagent connectivity based on a topological
neighborhood of interactions. The study of the connectedness of the swarm
signaling network reveals the profound relationship between group size and
number of interacting neighbors, which is found to be in good agreement with
field observations on flock of starlings [Ballerini et al. (2008) Proc. Natl.
Acad. Sci. USA, 105: 1232]. Using a dynamical model, we generate dynamic
collective behaviors enabling us to uncover that the swarm signaling network is
a homogeneous clustered small-world network, thus facilitating emergent
outcomes if connectedness is maintained. Resilience of the emergent consensus
is tested by introducing exogenous environmental noise, which ultimately
stresses how deeply intertwined are the swarm dynamics in the physical and
network spaces. The availability of the signaling network allows us to
analytically establish for the first time the number of driver agents necessary
to fully control the swarm dynamics
Synchronization in dynamical networks of locally coupled self-propelled oscillators
Systems of mobile physical entities exchanging information with their
neighborhood can be found in many different situations. The understanding of
their emergent cooperative behaviour has become an important issue across
disciplines, requiring a general conceptual framework in order to harvest the
potential of these systems. We study the synchronization of coupled oscillators
in time-evolving networks defined by the positions of self-propelled agents
interacting in real space. In order to understand the impact of mobility in the
synchronization process on general grounds, we introduce a simple model of
self-propelled hard disks performing persistent random walks in 2 space and
carrying an internal Kuramoto phase oscillator. For non-interacting particles,
self-propulsion accelerates synchronization. The competition between agent
mobility and excluded volume interactions gives rise to a richer scenario,
leading to an optimal self-propulsion speed. We identify two extreme dynamic
regimes where synchronization can be understood from theoretical
considerations. A systematic analysis of our model quantifies the departure
from the latter ideal situations and characterizes the different mechanisms
leading the evolution of the system. We show that the synchronization of
locally coupled mobile oscillators generically proceeds through coarsening
verifying dynamic scaling and sharing strong similarities with the phase
ordering dynamics of the 2 XY model following a quench. Our results shed
light into the generic mechanisms leading the synchronization of mobile agents,
providing a efficient way to understand more complex or specific situations
involving time-dependent networks where synchronization, mobility and excluded
volume are at play
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