118,475 research outputs found
Nonlinear analysis of dynamical complex networks
Copyright © 2013 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Complex networks are composed of a large number of highly interconnected dynamical units and therefore exhibit very complicated dynamics. Examples of such complex networks include the Internet, that is, a network of routers or domains, the World Wide Web (WWW), that is, a network of websites, the brain, that is, a network of neurons, and an organization, that is, a network of people. Since the introduction of the small-world network principle, a great deal of research has been focused on the dependence of the asymptotic behavior of interconnected oscillatory agents on the structural properties of complex networks. It has been found out that the general structure of the interaction network may play a crucial role in the emergence of synchronization phenomena in various fields such as physics, technology, and the life sciences
Randomized Consensus with Attractive and Repulsive Links
We study convergence properties of a randomized consensus algorithm over a
graph with both attractive and repulsive links. At each time instant, a node is
randomly selected to interact with a random neighbor. Depending on if the link
between the two nodes belongs to a given subgraph of attractive or repulsive
links, the node update follows a standard attractive weighted average or a
repulsive weighted average, respectively. The repulsive update has the opposite
sign of the standard consensus update. In this way, it counteracts the
consensus formation and can be seen as a model of link faults or malicious
attacks in a communication network, or the impact of trust and antagonism in a
social network. Various probabilistic convergence and divergence conditions are
established. A threshold condition for the strength of the repulsive action is
given for convergence in expectation: when the repulsive weight crosses this
threshold value, the algorithm transits from convergence to divergence. An
explicit value of the threshold is derived for classes of attractive and
repulsive graphs. The results show that a single repulsive link can sometimes
drastically change the behavior of the consensus algorithm. They also
explicitly show how the robustness of the consensus algorithm depends on the
size and other properties of the graphs
- …