Community detection is one of the most important problems in complex networks. Many algorithms have been proposed in the last decade, and most of them focus on the non-overlapping community structures in the early days. Overlapping and hierarchical structures are another two important properties...

A scaling theory is formulated in nonlinear Langevin equations with colored noise near the instability point from which the center of the initial distribution is deviated slightly. An intuitive derivation is given as well as perturbational calculations up to the infinite order of the noise....

We investigate an XY model on a four-layer triangular lattice with two ferromagnetic layers sandwiched by two antiferromagnetic layers by using Monte Carlo simulations. The chirality on the middle layers with ferromagnetic intralayer interactions shows very steep increase as temperature...

We investigate phase transitions of the XY model on a two-layer triangular lattice when interactions are competing, by using Monte Carlo simulations. For the system with a ferromagnetic interaction on one of two layers and an antiferromagnetic interaction on the other layer, we find two...

An SIS network model incorporating the influence of media coverage on transmission rate is formulated and analyzed. We calculate the basic reproduction number R0 by utilizing the local stability of the disease-free equilibrium. Our results show that the disease-free equilibrium is globally...

Time delay, accounting for constant incubation period or sojourn times in an infective state, widely exists in most biological systems like epidemiological models. However, the effect of time delay on spatial epidemic models is not well understood. In this paper, spatial pattern of an epidemic...

We investigate phase transitions of XY model on a three-layer triangular lattice by assuming that the intralayer interactions on the first and the third layer are antiferromagnetic and the one on the second layer ferromagnetic. We use Monte Carlo simulations and find that there are two critical...

In this paper, we propose and study an SIS epidemic model with multiple transmission routes on heterogeneous networks. We focus on the dynamical evolution of the prevalence. Through mathematical analysis, we obtain the basic reproduction number R0 by investigating the local stability of the...