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We introduce the sandpile model on multiplex networks with more than one type of edge and investigate its scaling and dynamical behaviors. We find that the introduction of multiplexity does not alter the scaling behavior of avalanche dynamics; the system is critical with an asymptotic power-law avalanche size distribution with an exponent τ = 3/2 on duplex random networks. The detailed cascade dynamics, however, is affected by the multiplex coupling. For example, higherdegree nodes such as hubs

We study the origin of scale invariance (SI) of the degree distribution in scale-free (SF) networks with a degree exponent γ under coarse graining. A varying number of vertices belonging to a community or a box in a fractal analysis is grouped into a supernode, where the box mass M follows a power-law distribution, PmM ~ M-\eta. The renormalized degree k′ of a supernode scales with its box mass M as k′ ~ Mθ. The two exponents η and θ can be nontrivial as η ≠ γ and θ < 1. They act as relevant par

We study the noise characteristics of stochastic oscillations in protein number dynamics of simple genetic oscillatory systems. Using the three-component negative feedback transcription regulatory system called the repressilator as a prototypical example, we quantify the degree of °uctuations in oscillation periods and amplitudes, as well as the noise propagation along the regulatory cascade in the stable oscillation regime via dynamic Monte Carlo simulations. For the single protein-species leve

We collect empirical data for a coauthorship network of scientists working on the subject of complex networks for 103 months, starting from the initial point of its evolution. Such a data set enables us to study the evolution of a complex network from the seed. Based on the statistics of evolution rates of various types of edges obtained from the empirical data, we find that the edge-strength enhancement, cluster growth, and creation of new clusters are dominant processes occurring in the evolut