Detecting overlapping communities in complex networks using non-cooperative games.

Detecting communities in complex networks is of paramount importance, and its wide range of real-life applications in various areas has caused a lot of attention to be paid to it, and many efforts have been made to have efficient and accurate algorithms for this purpose. In this paper, we proposed a non-cooperative game theoretic-based algorithm that is able to detect overlapping communities. In this algorithm, nodes are regarded as players, and communities are assumed to be groups of players with similar strategies.

Exploration-imitation competition in well-mixed and structured populations.

Social physics is the mathematical study of how the flow of ideas can change the behavior of individuals. Models in social physics include processes for searching after new ideas and dispersing them inside the population. The present paper makes use of exploration and imitation processes for the mentioned purpose.

Multi-strategy evolutionary games: A Markov chain approach.

Interacting strategies in evolutionary games is studied analytically in a well-mixed population using a Markov chain method. By establishing a correspondence between an evolutionary game and Markov chain dynamics, we show that results obtained from the fundamental matrix method in Markov chain dynamics are equivalent to corresponding ones in the evolutionary game. In the conventional fundamental matrix method, quantities like fixation probability and fixation time are calculable.

Fixation time in evolutionary graphs: A mean-field approach.

Using an analytical method we calculate average conditional fixation time of mutants in a general graph-structured population of two types of species. The method is based on Markov chains and uses a mean-field approximation to calculate the corresponding transition matrix. Analytical results are compared with the results of simulation of the Moran process on a number of network structures.

Separation of cyclic and starlike hierarchical dominance in evolutionary matrix games.

We study antisymmetric components of matrices characterizing pair interactions in multistrategy evolutionary games. Based on the dyadic decomposition of matrices we distinguish cyclic and starlike hierarchical dominance in the appropriate components. In the symmetric matrix games the strengths of these elementary components are determined.

Analytical calculation of average fixation time in evolutionary graphs.

The ability of a mutant individual to overtake the whole of a population is one of the fundamental problems in evolutionary dynamics. Fixation probability and Average Fixation Time (AFT) are two important parameters to quantify this ability. In this paper we introduce an analytical approach for exact calculation of AFT.

Noise-induced synchronization in small world networks of phase oscillators.

A small-world (SW) network of similar phase oscillators, interacting according to the Kuramoto model, is studied numerically. It is shown that deterministic Kuramoto dynamics on SW networks has various stable stationary states. This can be attributed to the so-called defect patterns in an SW network, which it inherits from deformation of helical patterns in its regular parent.

Stability of synchronized states in networks of phase oscillators.

The stability of synchronized states (frequency locked states) in networks of phase oscillators is investigated for several network topologies. It is shown that for some topologies there is more than one stable synchronized state according to the sign of coupling strength between oscillators. It is also shown that in some cases the synchronized state corresponds to zero order parameter.