3,542 research outputs found
Scaling of internode distances in weighted complex networks
We extend the previously observed scaling equation connecting the internode
distances and nodes' degrees onto the case of weighted networks. We show that
the scaling takes a similar form in the empirical data obtained from networks
characterized by different relations between node's strength and its degree. In
the case of explicit equation for s(k) (e.g. linear or scale-free), the new
coefficients of scaling equation can be easily obtained. We support our
analysis with numerical simulations for Erdos-Renyi random graphs with
different weight distributions.Comment: 9 pages, 4 figures, submitted to International Journal of Modern
Physics
A threshold model of financial markets
We proposed a model of interacting market agents based on the Ising spin
model. The agents can take three actions: "buy," "sell," or "stay inactive." We
defined a price evolution in terms of the system magnetization. The model
reproduces main stylized facts of real markets such as: fat-tailed distribution
of returns and volatility clustering
Anomalous oscillations of average transient lifetimes near crises
It is common that the average length of chaotic transients appearing as a
consequence of crises in dynamical systems obeys a power low of scaling with
the distance from the crisis point. It is, however, only a rough trend; in some
cases considerable oscillations can be superimposed on it. In this letter we
report anomalous oscillations due to the intertwined structure of basins of
attraction. We also present a simple geometrical model that gives an estimate
of the period and amplitude of these oscillations. The results obtained within
the model coincide with those yielded by computer simulations of a kicked spin
model and the Henon map.Comment: 5 pages, 4 figure
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