Abstract:
Complex networks are characterized by several topological properties: degree distribution, clustering coefficient, average shortest path length, etc. Using a simple model to generate scale-free networks embedded on geographical space, we analyze the relationship between topological properties of the network and attributes (fitness and location) of the vertices in the network. We find there are two crossovers for varying the scaling exponent of the fitness distribution.

Abstract:
We investigate how network structure influences evolutionary games on networks. We extend the pair approximation to study the effects of degree fluctuation and clustering of the network. We find that a larger fluctuation of the degree is equivalent to a larger mobility of the players. In addition, a larger clustering coefficient is equivalent to a smaller number of neighbors.

Abstract:
We propose a new method to investigate collective behavior in a network of globally coupled chaotic elements generated by a tent map. In the limit of large system size, the dynamics is described with the nonlinear Frobenius-Perron equation. This equation can be transformed into a simple form by making use of the piecewise linear nature of the individual map. Our method is applied successfully to the analyses of stability of collective stationary states and their bifurcations.

Abstract:
It is well known that random multiplicative processes generate power-law probability distributions. We study how the spatio-temporal correlation of the multipliers influences the power-law exponent. We investigate two sources of the time correlation: the local environment and the global environment. In addition, we introduce two simple models through which we analytically and numerically show that the local and global environments yield different trends in the power-law exponent.

Abstract:
Spreading phenomena are ubiquitous in nature and society. For example, disease, rumor, and information spread over underlying social and information networks. It is well known that there is no threshold for epidemic models on scale-free networks; this suggests that disease can spread on such networks, regardless of how low the contact rate may be. In this paper, I consider six models with different contact and propagation mechanisms. Each model is analyzed by degree-based mean-field theory. I show that the presence or absence of an outbreak threshold depends on the contact and propagation mechanism.

Abstract:
This study investigates the influence of lattice structure in evolutionary games. The snowdrift games is considered in networks with high clustering coefficients, that use four different strategy-updating. Analytical conjectures using pair approximation were compared with the numerical results. Results indicate that general statements asserting that the lattice structure enhances cooperation are misleading.

Abstract:
We study a generalization of globally coupled maps, where the elements are updated with probability $p$. When $p$ is below a threshold $p_c$, the collective motion vanishes and the system is the stationary state in the large size limit. We present the linear stability analysis.

Abstract:
We study a stochastic linear discrete metapolulation model to understand the effect of risk spreading by dispersion. We calculate analytically the stable distribution of populations that live in different habitats. The result shows that the simultaneous distribution of the populations has a complicated self-similar structure, but a population at each habitat follows a log-normal distribution.

Abstract:
We study a stochastic matrix model to understand the mechanics of risk-spreading (or bet-hedging) by dispersion. Such model has been mostly dealt numerically except for well-mixed case, so far. Here, we present an analytical result, which shows that optimal dispersion leads to Zipf's law. Moreover, we found that the arithmetic ensemble average of the total growth rate converges to the geometric one, because the sample size is finite.

Abstract:
It has not been known whether preferential dispersal is adaptive in fluctuating environments. We investigate the effect of preferential and random dispersals in bet-hedging systems by using a discrete stochastic metapopulation model, where each site fluctuates between good and bad environments with temporal correlation. To explore the optimal migration pattern, an analytical estimation of the total growth is derived by mean field approximation. We found that the preference for fertile sites is disadvantageous when transportation among sites has a cost or the sensitivity of preference is high.