Agreement Dynamics of Memory-Based Naming Game with Forgetting Curve of Ebbinghaus

We propose a memory-based naming game （MBNG） model which is like some previous opinion propagation models. with two-state variables in full-connected networks, It is found that this model is deeply affected by the memory decision parameter, and then its dynamical behaviour can be partly analysed by using numerical simulation and analytical argument. We also report a modified MBNG model with the forgetting curve of Ebbinghaus in the memory. With deletion of one parameter in the MBNG model, it can converge to success rate S（t） = 1 and the average sum E（t） is decided by the size of network N.     

Agreement dynamics of finite-memory language games on networks

We propose a Finite-Memory Naming Game (FMNG) model with respect to the bounded rationality of agents or finite resources for information storage in communication systems. We study its dynamics on several kinds of complex networks, including random networks, small-world networks and scale-free networks. We focus on the dynamics of the FMNG affected by the memory restriction as well as the topological properties of the networks. Interestingly, we found that the most important quantity, the convergence time of reaching the consensus, shows some non-monotonic behaviors by varying the average degrees of the networks with the existence of the fastest convergence at some specific average degrees. We also investigate other main quantities, such as the success rate in negotiation, the total number of words in the system and the correlations between agents of full memory and the total number of words, which clearly explain the nontrivial behaviors of the convergence. We provide some analytical results which help better understand the dynamics of the FMNG. We finally report a robust scaling property of the convergence time, which is regardless of the network structure and the memory restriction.     

Effect of imitation in evolutionary minority game on small-world networks

The system performance in an evolutionary minority game with imitation on small-world networks is studied. Numerical results show that system performance positively correlates with the clustering coefficients. The domain structure of the agents’ strategies can be used to give a qualitative explanation for it. We also find that the time series of the reduced variance σ²/N could have a phasic evolution from a metastable state (two crowds are formed but the distribution of their probabilities does not peak at p≈0 and p≈1) to a steadystate (the two crowds evolve into a crowd and an anticrowd with the distribution of their probabilities peaking at p≈0 and p≈1).     

Sandpile on directed small-world networks

We numerically investigate the avalanche dynamics of the Bak-Tang-Wiesenfeld sandpile model on directed small-world networks. We find that the avalanche size and duration distribution follow a power law for all rewiring probabilities p. Specially, we find that, approaching the thermodynamic limit (L→∞), the values of critical exponents do not depend on p and are consistent with the mean-field solution in Euclidean space for any p>0. In addition, we measure the dynamic exponent in the relation between avalanche size and avalanche duration and find that the values of the dynamic exponents are also consistent with the mean-field values for any p>0.     

Robustness of heterogeneous complex networks

In this paper we study the robustness of heterogeneous preferential attachment networks. The robustness of a network measures its structural tolerance to the random removal of nodes and links. We numerically analyze the influence of the affinity parameters on a set of ensemble-averaged robustness metrics. We show that the presence of heterogeneity does not fundamentally alter the smooth nature of the fragmentation process of the models. We also show that a moderate level of locality translates into slight improvements in the robustness metrics, which prompts us to conjecture an evolutionary argument for the existence of real networks with power-law scaling in their connectivity and clustering distributions.     

Local affinity in heterogeneous growing networks

In this paper we present a study of the influence of local affinity in heterogeneous preferential attachment (PA) networks. Heterogeneous PA models are a generalization of the Barabási-Albert model to heterogeneous networks, where the affinity between nodes biases the attachment probability of links. Threshold models are a class of heterogeneous PA models where the affinity between nodes is inversely related to the distance between their states. We propose a generalization of threshold models where network nodes have individual affinity functions, which are then combined to yield the affinity of each potential interaction. We analyze the influence of the affinity functions in the topological properties averaged over a network ensemble. The network topology is evaluated through the distributions of connectivity degrees, clustering coefficients and geodesic distances. We show that the relaxation of the criterion of a single global affinity still leads to a reasonable power-law scaling in the connectivity and clustering distributions under a wide spectrum of assumptions. We also show that the richer behavior of the model often exhibits a better agreement with the empirical observations on real networks.     

Lamellar pattern formation in small-world media

Numerical and analytical techniques are used to investigate the effects of quenched disorder of small-world networks on the phase ordering dynamics of lamellar patterns as modeled by the Swift-Hohenberg equation. Morphologies for small and large values of the network randomness are quite different. It is found that addition of shortcuts to an underlying regular lattice makes the growth of domains evolving from random initial conditions much slower at late times. As the randomness increases, the evolution is eventually frozen.     

Relaxation dynamics of aftershocks after large volatility shocks in the SSEC index

The relaxation dynamics of aftershocks after large volatility shocks are investigated based on two high-frequency data sets of the Shanghai Stock Exchange Composite (SSEC) index. Compared with previous relevant work, we have defined main financial shocks based on large volatilities rather than large crashes. We find that the occurrence rate of aftershocks with the magnitude exceeding a given threshold for both daily volatility (constructed using 1-minute data) and minutely volatility (using intra-minute data) decays as a power law. The power-law relaxation exponent increases with the volatility threshold and is significantly greater than 1. Taking financial volatility as the counterpart of seismic activity, the power-law relaxation in financial volatility deviates remarkably from the Omori law in Geophysics.     

Coevolutionary extremal dynamics on gasket fractal

We considered a Bak-Sneppen model on a Sierpinski gasket fractal. We calculated the avalanche size distribution and the distribution of distances between subsequent minimal sites. To observe the temporal correlations of the avalanche, we estimated the return time distribution, the first-return time, and the all-return time distribution. The avalanche size distribution follows the power law, P(s)∼s−τ, with the exponent τ=1.004(7). The distribution of jumping sites also follows the power law, P(r)∼r−π, with the critical exponent π=4.12(4). We observe the periodic oscillation of the distribution of the jumping distances which originated from the jumps of the level when the minimal site crosses the stage of the fractal. The first-return time distribution shows the power law, Pf(t)∼t−τf, with the critical exponent τf=1.418(7). The all-return time distribution is also characterized by the power law, Pa(t)∼t−τa, with the exponent τa=0.522(4). The exponents of the return time satisfy the scaling relation τf+τa=2 for τf?2.     

Statistical Property and Model for the Inter-Event Time of Terrorism Attacks

The inter-event time of terrorism attack events is investigated by empirical data and model analysis. Empirical evidence shows that it follows a scale-free property. In order to understand the dynamic mechanism of such a statistical feature, an opinion dynamic model with a memory effect is proposed on a two-dimensional lattice network. The model mainly highlights the role of individual social conformity and self-affirmation psychology. An attack event occurs when the order parameter indicating the strength of public opposition opinion is smaller than a critical value. Ultimately, the model can reproduce the same statistical property as the empirical data and gives a good understanding for the possible dynamic mechanism of terrorism attacks.     

The network of commuters in London

We have studied the directed and weighted network in which the wards of London are vertices and two vertices are connected whenever there is at least one person commuting to work from one ward to another. Remarkably the in-strength and in-degree distribution tail is a power law with exponent around −2, while the out-strength and out-degree distribution tail is exponential. We propose a simple square lattice model to explain the observed empirical behaviour.     

Community structure in Congressional cosponsorship networks

We study the United States Congress by constructing networks between Members of Congress based on the legislation that they cosponsor. Using the concept of modularity, we identify the community structure of Congressmen, who are connected via sponsorship/cosponsorship of the same legislation. This analysis yields an explicit and conceptually clear measure of political polarization, demonstrating a sharp increase in partisan polarization which preceded and then culminated in the 104th Congress (1995-1996), when Republicans took control of both chambers of Congress. Although polarization has since waned in the U.S. Senate, it remains at historically high levels in the House of Representatives.     

Emergence of scale-free behavior in networks from limited-horizon linking and cost trade-offs

We study network growth from a fixed set of initially isolated nodes placed at random on the surface of a sphere. The growth mechanism we use adds edges to the network depending on strictly local gain and cost criteria. Only nodes that are not too far apart on the sphere may be considered for being joined by an edge. Given two such nodes, the joining occurs only if the gain of doing it surpasses the cost. Our model is based on a multiplicative parameter λ that regulates, in a function of node degrees, the maximum geodesic distance that is allowed between nodes for them to be considered for joining. For n nodes distributed uniformly on the sphere, and for within limits that depend on cost-related parameters, we have found that our growth mechanism gives rise to power-law distributions of node degree that are invariant for constant . We also study connectivity- and distance-related properties of the networks.     

Dynamics-driven evolution to structural heterogeneity in complex networks

The mutual influence of dynamics and structure is a central issue in complex systems. In this paper we study by simulation slow evolution of network under the feedback of a local-majority-rule opinion process. If performance-enhancing local mutations have higher chances of getting integrated into its structure, the system can evolve into a highly heterogeneous small-world with a global hub (whose connectivity is proportional to the network size), strong local connection correlations and power-law-like degree distribution. Networks with better dynamical performance are achieved if structural evolution occurs much slower than the network dynamics. Structural heterogeneity of many biological and social dynamical systems may also be driven by various dynamics-structure coupling mechanisms.     

Spectral methods and cluster structure in correlation-based networks

We investigate how in complex systems the eigenpairs of the matrices derived from the correlations of multichannel observations reflect the cluster structure of the underlying networks. For this we use daily return data from the NYSE and focus specifically on the spectral properties of weight W_ij=|C|_ij−δ_ij and diffusion matrices D_ij=W_ij/s_j−δ_ij, where C_ij is the correlation matrix and s_i=∑_jW_ij the strength of node j. The eigenvalues (and corresponding eigenvectors) of the weight matrix are ranked in descending order. As in the earlier observations, the first eigenvector stands for a measure of the market correlations. Its components are, to first approximation, equal to the strengths of the nodes and there is a second order, roughly linear, correction. The high ranking eigenvectors, excluding the highest ranking one, are usually assigned to market sectors and industrial branches. Our study shows that both for weight and diffusion matrices the eigenpair analysis is not capable of easily deducing the cluster structure of the network without a priori knowledge. In addition we have studied the clustering of stocks using the asset graph approach with and without spectrum based noise filtering. It turns out that asset graphs are quite insensitive to noise and there is no sharp percolation transition as a function of the ratio of bonds included, thus no natural threshold value for that ratio seems to exist. We suggest that these observations can be of use for other correlation based networks as well.     

Scaling relation for earthquake networks

The scaling relation, 2γ−δ=1, for the exponents of the power-law connectivity distribution, γ, and the power-law eigenvalue distribution of the adjacency matrix, δ, is theoretically predicted to be fulfilled by a locally treelike scale-free network in the “effective medium approximation” (i.e., an analog of the mean field approximation). Here, it is shown that such a relation holds well for the reduced simple earthquake networks (i.e., the network without tadpole-loops and multiple edges) constructed from the seismic data taken from California and Japan. This validates the goodness of the effective medium approximation in the earthquake networks and is consistent with the hierarchical organization of the networks. The present result may be useful for modeling seismicity on complex networks.     

Ideal free distribution or dynamic game? An agent-based simulation study of trawling strategies with varying information

An ecological economic model of trawling is presented to demonstrate the effect of trawling location choice strategy on net input (rate of economic gain of fish caught per time spent less costs). Fishing location choice is considered to be a dynamic process whereby trawlers chose from among a repertoire of plastic strategies that they modify if their gains fall below a fixed proportion of the mean gains of the fleet as a whole. The distribution of fishing across different areas of a fishery follows an approximate ideal free distribution (IFD) with varying noise due to uncertainty. The least-productive areas are not utilised because initial net input never reaches the mean yield of better areas subject to competitive exploitation. In cases, where there is a weak temporal autocorrelation between fish stocks in a specific location, a plastic strategy of local translocation between trawls mixed with longer-range translocation increases realised input. The trawler can change its translocation strategy in the light of information about recent trawling success compared to its long-term average but, in contrast to predictions of the Marginal Value Theorem (MVT) model, does not know for certain what it will find by moving, so may need to sample new patches. The combination of the two types of translocation mirrored beam-trawling strategies used by the Dutch fleet and the resultant distribution of trawling effort is confirmed by analysis of historical effort distribution of British otter trawling fleets in the North Sea. Fisheries exploitation represents an area where dynamic agent-based adaptive models may be a better representation of the economic dynamics of a fleet than classically inspired optimisation models.     

New tools for characterizing swarming systems: A comparison of minimal models

We compare three simple models that reproduce qualitatively the emergent swarming behavior of bird flocks, fish schools, and other groups of self-propelled agents by using a new set of diagnosis tools related to the agents’ spatial distribution. Two of these correspond in fact to different implementations of the same model, which had been previously confused in the literature. All models appear to undergo a very similar order-to-disorder phase transition as the noise level is increased if we only compare the standard order parameter, which measures the degree of agent alignment. When considering our novel quantities, however, their properties are clearly distinguished, unveiling previously unreported qualitative characteristics that help determine which model best captures the main features of realistic swarms. Additionally, we analyze the agent clustering in space, finding that the distribution of cluster sizes is typically exponential at high noise, and approaches a power-law as the noise level is reduced. This trend is sometimes reversed at noise levels close to the phase transition, suggesting a non-trivial critical behavior that could be verified experimentally. Finally, we study a bi-stable regime that develops under certain conditions in large systems. By computing the probability distributions of our new quantities, we distinguish the properties of each of the coexisting metastable states. Our study suggests new experimental analyses that could be carried out to characterize real biological swarms.     

Role of Clustering Coefficient on Cooperation Dynamics in Homogeneous Networks

Based on previous works, we give further investigations on the Prisoners＇ Dilemma Game （PDG） on two different types of homogeneous networks, i.e. the homogeneous small-world network （HSWN） and the regular ring graph. We find that the so-called resonance-like character can occur on both the networks. Different from the viewpoint in previous publications, we think the small-world effect may be unnecessary to produce this character. Therefore, over these two types of networks, we suggest a common understanding in the viewpoint of clustering coefficient. Detailed simulation results can sustain our viewpoint quite well. Furthermore, we investigate the Snowdrift Game （SG） on the same networks. The difference between the outputs of the PDG and the SG can also sustain our viewpoint.     

Limited ability driven phase transitions in the coevolution process in Axelrod's model

We study the coevolution process in Axelrod's model by taking into account of agents' abilities to access information, which is described by a parameter α to control the geographical range of communication. We observe two kinds of phase transitions in both cultural domains and network fragments, which depend on the parameter α. By simulation, we find that not all rewiring processes pervade the dissemination of culture, that is, a very limited ability to access information constrains the cultural dissemination, while an exceptional ability to access information aids the dissemination of culture. Furthermore, by analyzing the network characteristics at the frozen states, we find that there exists a stage at which the network develops to be a small-world network with community structures.