1,700 research outputs found
The Hutchinson-Barnsley theory for generalized iterated function systems by means of infinite iterated function systems
The study of generalized iterated function systems (GIFS) was introduced by
Mihail and Miculescu in 2008. We provide a new approach to study those systems
as the limit of the Hutchinson-Barnsley theory for infinite iterated function
systems (IIFS) which was developed by many authors in the last years. We show
that any attractor of a contractive generalized iterated function system is the
limit w.r.t Hausdorff-Pompeiu metric of attractors of contractive infinite
iterated function systems. We also prove that any Hutchinson measure for a
contractive generalized iterated function system with probabilities is the
limit w.r.t. the Monge-Kantorovich metric of the Hutchinson measures for
contractive infinite iterated function systems with probabilities.Comment: 14 page
Evolutionary prisoner's dilemma game on a square lattice
A simplified prisoner's game is studied on a square lattice when the players
interacting with their neighbors can follow only two strategies: to cooperate
(C) or to defect (D) unconditionally. The players updated in a random sequence
have a chance to adopt one of the neighboring strategies with a probability
depending on the payoff difference. Using Monte Carlo simulations and dynamical
cluster techniques we study the density of cooperators in the stationary
state. This system exhibits a continuous transition between the two absorbing
state when varying the value of temptation to defect. In the limits
and 1 we have observed critical transitions belonging to the universality class
of directed percolation.Comment: 6 pages including 6 figure
Multifractal analysis of weighted networks by a modified sandbox algorithm
Complex networks have attracted growing attention in many fields. As a
generalization of fractal analysis, multifractal analysis (MFA) is a useful way
to systematically describe the spatial heterogeneity of both theoretical and
experimental fractal patterns. Some algorithms for MFA of unweighted complex
networks have been proposed in the past a few years, including the sandbox (SB)
algorithm recently employed by our group. In this paper, a modified SB
algorithm (we call it SBw algorithm) is proposed for MFA of weighted
networks.First, we use the SBw algorithm to study the multifractal property of
two families of weighted fractal networks (WFNs): "Sierpinski" WFNs and "Cantor
dust" WFNs. We also discuss how the fractal dimension and generalized fractal
dimensions change with the edge-weights of the WFN. From the comparison between
the theoretical and numerical fractal dimensions of these networks, we can find
that the proposed SBw algorithm is efficient and feasible for MFA of weighted
networks. Then, we apply the SBw algorithm to study multifractal properties of
some real weighted networks ---collaboration networks. It is found that the
multifractality exists in these weighted networks, and is affected by their
edge-weights.Comment: 15 pages, 6 figures. Accepted for publication by Scientific Report
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