Beomjun Kim

A two-dimensional small-world-type network, subject to spatial prisoners' dilemma dynamics and containing an influential node defined as a special node, with a finite density of directed random links to the other nodes in the network, is numerically investigated. It is shown that the degree of cooperation does not remain at a steady state level but displays a punctuated equilibrium-type behavior manifested by the existence of sudden breakdowns of cooperation. The breakdown of cooperation is link

We numerically investigate the scale-free network model of Barabási and Albert [A. L. Barabási and R. Albert, Science 286, 509 (1999)] through the use of various path finding strategies. In real networks, global network information is not accessible to each vertex, and the actual path connecting two vertices can sometimes be much longer than the shortest one. A generalized diameter depending on the actual path finding strategy is introduced, and a simple strategy, which utilizes only local infor

The performance of the Hopfield neural network model is numerically studied on various complex networks, such as the Watts-Strogatz network, the Barabási-Albert network, and the neuronal network of Caenorhabditis elegans. Through the use of a systematic way of controlling the clustering coefficient, with the degree of each neuron kept unchanged, we find that the networks with the lower clustering exhibit much better performance. The results are discussed in the practical viewpoint of application

The phase transition in the XY model on one-dimensional small-world networks is investigated by means of Monte Carlo simulations. It is found that long-range order is present at finite temperatures, even for very small values of the rewiring probability, suggesting a finite-temperature transition for any nonzero rewiring probability. Nature of the phase transition is discussed in comparison with the globally coupled XY model.

We perform a renormalization-grouplike numerical analysis of geographically embedded complex networks on a two-dimensional square lattice. At each step of the coarse-graining procedure, the four vertices on each 2x2 square box are merged to a single vertex, resulting in a coarse-grained system of smaller size. Repetition of the process leads to the observation that the coarse-graining procedure does not alter the qualitative characteristics of the original scale-free network, which opens the pos

Two-dimensional $\mathrm{XY}$ models with resistively shunted junction (RSJ) dynamics and time dependent Ginzburg-Landau (TDGL) dynamics are simulated and it is verified that the vortex response is well described by the Minnhagen phenomenology for both types of dynamics. Evidence is presented supporting that the dynamical critical exponent z in the low-temperature phase is given by the scaling prediction (expressed in terms of the Coulomb gas temperature ${T}^{\mathrm{CG}}$ and the vortex renorm

To probe the connection between the dynamic phase transition and stochastic resonance, we study the mean-field kinetic Ising model and the two-dimensional Josephson-junction array in the presence of appropriate oscillating magnetic fields. Observed in both systems are {\it double} stochastic resonance peaks, one below and the other above the dynamic transition temperature, the appearance of which is argued to be a generic property of the system with a continuous dynamic phase transition. In part

We study numerically quantum diffusion of a particle on small-world networks by integrating the time-dependent Schr\"odinger equation with a localized initial state. The participation ratio, which corresponds to the number of visited sites in the case of classical diffusion, as a function of time is measured and the corresponding diffusion time, $\ensuremath{\tau}$ is computed. In a local regular network, i.e., in the network with the rewiring probability $p=0,$ the diffusion time depends on the