Diffusive Capture Process on Complex Networks

Details Diffusive Capture Process on Complex Networks Diffusive Capture Process on Complex Networks

2006-03-24

arxiv.org/abs/cond-mat/0603647v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

9 pages, 6 figures

Scientific paper

10.1103/PhysRevE.74.046118

We study the dynamical properties of a diffusing lamb captured by a diffusing lion on the complex networks with various sizes of $N$. We find that the life time $ of a lamb scales as \sim N$ and the survival probability $S(N\to \infty,t)$ becomes finite on scale-free networks with degree exponent $\gamma>3$. However, $S(N,t)$ for $\gamma<3$ has a long-living tail on tree-structured scale-free networks and decays exponentially on looped scale-free networks. It suggests that the second moment of degree distribution $ is the relevant factor for the dynamical properties in diffusive capture process. We numerically find that the normalized number of capture events at a node with degree $k$, $n(k)$, decreases as $n(k)\sim k^{-\sigma}$. When $\gamma<3$, $n(k)$ still increases anomalously for $k\approx k_{max}$. We analytically show that $n(k)$ satisfies the relation $n(k)\sim k^2P(k)$ and the total number of capture events $N_{tot}$ is proportional to $, which causes the $\gamma$ dependent behavior of $S(N,t)$ and $.

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