4 research outputs found
Unanimity Rule on networks
We introduce a model for innovation-, evolution- and opinion dynamics whose
spreading is dictated by unanimity rules, i.e. a node will change its (binary)
state only if all of its neighbours have the same corresponding state. It is
shown that a transition takes place depending on the initial condition of the
problem. In particular, a critical number of initially activated nodes is
needed so that the whole system gets activated in the long-time limit. The
influence of the degree distribution of the nodes is naturally taken into
account. For simple network topologies we solve the model analytically, the
cases of random, small-world and scale-free are studied in detail.Comment: 7 pages 4 fig
Solution of the Unanimity Rule on exponential, uniform and scalefree networks: A simple model for biodiversity collapse in foodwebs
We solve the Unanimity Rule on networks with exponential, uniform and
scalefree degree distributions. In particular we arrive at equations relating
the asymptotic number of nodes in one of two states to the initial fraction of
nodes in this state. The solutions for exponential and uniform networks are
exact, the approximation for the scalefree case is in perfect agreement with
simulation results. We use these solutions to provide a theoretical
understanding for experimental data on biodiversity loss in foodwebs, which is
available for the three network types discussed. The model allows in principle
to estimate the critical value of species that have to be removed from the
system to induce its complete collapse.Comment: 4 pages, 3 fig
Opinion Formation in Laggard Societies
We introduce a statistical physics model for opinion dynamics on random
networks where agents adopt the opinion held by the majority of their direct
neighbors only if the fraction of these neighbors exceeds a certain threshold,
p_u. We find a transition from total final consensus to a mixed phase where
opinions coexist amongst the agents. The relevant parameters are the relative
sizes in the initial opinion distribution within the population and the
connectivity of the underlying network. As the order parameter we define the
asymptotic state of opinions. In the phase diagram we find regions of total
consensus and a mixed phase. As the 'laggard parameter' p_u increases the
regions of consensus shrink. In addition we introduce rewiring of the
underlying network during the opinion formation process and discuss the
resulting consequences in the phase diagram.Comment: 5 pages, eps fig
Coexistence of opposite opinions in a network with communities
The Majority Rule is applied to a topology that consists of two coupled
random networks, thereby mimicking the modular structure observed in social
networks. We calculate analytically the asymptotic behaviour of the model and
derive a phase diagram that depends on the frequency of random opinion flips
and on the inter-connectivity between the two communities. It is shown that
three regimes may take place: a disordered regime, where no collective
phenomena takes place; a symmetric regime, where the nodes in both communities
reach the same average opinion; an asymmetric regime, where the nodes in each
community reach an opposite average opinion. The transition from the asymmetric
regime to the symmetric regime is shown to be discontinuous.Comment: 14 pages, 4 figure