Evolutionary Prisoner's Dilemma Game Based on Pursuing Higher Average Payoff

We investigate the prisoner＇s dilemma game based on a new rule： players will change their current strategies to opposite strategies with some probability if their neighbours＇ average payoffs are higher than theirs. Compared with the cases on regular lattices （RL） and Newman-Watts small world network （NW）, cooperation can be best enhanced on the scale-free Barabasi-Albert network （BA）. It is found that cooperators are dispersive on RL network, which is different from previously reported results that cooperators will form large clusters to resist the invasion of defectors. Cooperative behaviours on the BA network are discussed in detail. It is found that large-degree individuals have lower cooperation level and gain higher average payoffs than that of small-degree individuals. In addition, we find that small-degree individuals more frequently change strategies than do large- degree individuals.     

A neighbourhood evolving network model

Many social, technological, biological and economical systems are best described by evolved network models. In this short Letter, we propose and study a new evolving network model. The model is based on the new concept of neighbourhood connectivity, which exists in many physical complex networks. The statistical properties and dynamics of the proposed model is analytically studied and compared with those of Barabási–Albert scale-free model. Numerical simulations indicate that this network model yields a transition between power-law and exponential scaling, while the Barabási–Albert scale-free model is only one of its special (limiting) cases. Particularly, this model can be used to enhance the evolving mechanism of complex networks in the real world, such as some social networks development.     

Spatial Pattern of an Epidemic Model with Cross-diffusion

Pattern formation of a spatial epidemic model with both self- and cross-diffusion is investigated. From the Turing theory, it is well known that Turing pattern formation cannot occur for the equal self-diffusion coefficients. However, combined with cross-diffusion, the system will show emergence of isolated groups, i.e., stripe-like or spotted or coexistence of both, which we show by both mathematical analysis and numerical simulations. Our study shows that the interaction of self- and cross-diffusion can be considered as an important mechanism for the appearance of complex spatiotemporal dynamics in epidemic models.     

S-curve networks and an approximate method for estimating degree distributions of complex networks

In the study of complex networks almost all theoretical models have the property of infinite growth,but the size of actual networks is finite.According to statistics from the China Internet IPv4(Internet Protocol version 4) addresses,this paper proposes a forecasting model by using S curve(logistic curve).The growing trend of IPv4 addresses in China is forecasted.There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6.Based on the laws of IPv4 growth,that is,the bulk growth and the finitely growing limit,it proposes a finite network model with a bulk growth.The model is said to be an S-curve network.Analysis demonstrates that the analytic method based on uniform distributions(i.e.,Barab’asi-Albert method) is not suitable for the network.It develops an approximate method to predict the growth dynamics of the individual nodes,and uses this to calculate analytically the degree distribution and the scaling exponents.The analytical result agrees with the simulation well,obeying an approximately power-law form.This method can overcome a shortcoming of Baraba’si-Albert method commonly used in current network research.     

A limited resource model of fault-tolerant capability against cascading failure of complex network

We propose a novel capacity model for complex networks against cascading failure. In this model, vertices with both higher loads and larger degrees should be paid more extra capacities, i.e. the allocation of extra capacity on vertex i will be proportional to k_i ^γ , where k_i is the degree of vertex i and γ > 0 is a free parameter. We have applied this model on Barabási-Albert network as well as two real transportation networks, and found that under the same amount of available resource, this model can achieve better network robustness than previous models.     

n-ary fragmentation model with nearest point flaw and maximal net force fracture

Through the distinction between “real” and “virtual” links between the nodes of a graph, we develop a set of simple rules leading to scale-free networks with a tunable degree distribution exponent. Albeit sharing some similarities with preferential attachment, our procedure is both faster than a naïve implementation of the Barabási and Albert model and exhibits different clustering properties. The model is thoroughly studied numerically and suggests that reducing the set of partners a node can connect to is important in seizing the diversity of scale-free structures.     

A self-organizing shortest path finding strategy on complex networks

The shortcomings of traditional methods to find the shortest path are revealed, and a strategy of finding the self-organizing shortest path based on thermal flux diffusion on complex networks is presented. In our method, the shortest paths between the source node and the other nodes are found to be self-organized by comparing node temperatures. The computation complexity of the method scales linearly with the number of edges on underlying networks. The effects of the method on several networks, including a regular network proposed by Ravasz and Barabási which is called the RB network, a real network, a random network proposed by Ravasz and Barabási which is called the ER network and a scale-free network, are also demonstrated. Analytic and simulation results show that the method has a higher accuracy and lower computational complexity than the conventional methods.     

Spatial Games Based on Pursuing the Highest Average Payoff

We propose a strategy updating mechanism based on pursuing the highest average payoff to investigate the prisoner＇s dilemma game and the snowdrift game. We apply the new rule to investigate cooperative behaviours on regular, small-world, scale-free networks, and find spatial structure can maintain cooperation for the prisoner＇s dilemma game. fn the snowdrift game, spatial structure can inhibit or promote cooperative behaviour which depends on payoff parameter. We further study cooperative behaviour on scale-free network in detail. Interestingly, non-monotonous behaviours observed on scale-free network with middle-degree individuals have the lowest cooperation level. We also find that large-degree individuals change their strategies more frequently for both games.     

A harmonious unifying hybrid preferential model and its universal properties for complex dynamical networks

To describe the real world which is a harmonious unification world with both de- terminism and randomness, we propose a harmonious unifying hybrid preferential model (HUHPM) of a certain class of complex dynamical networks. HUHPM is gov- erned only by the total hybrid ratio d/r according to the practical need. As some typical examples, the concepts and methods of the HUHPM are applied to the un-weighted BA model proposed by Barabási et al., the weighted BBV model pro- posed by Barat et al. and the weighted TDE model proposed by Wang et al. to get the so-called HUHPM-BA network, HUHPM-BBV network and HUHPM-TDE network. These HUHPM networks are investigated both analytically and numerically. It is found that the HUHPM reveals several universal properties, which more approach to the real-world networks for both un-weighted and weighted networks and have potential for applications.     

Stability and dynamical properties of material flow systems on random networks

The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are characteristic of flow networks in economic, ecological and biological systems. Based on results from random matrix theory, we work out the phase diagram of such systems defined on extensively connected random graphs, and study in detail how the choice of control policies and the network structure affects stability. We also present results for more complex topologies of the underlying graph, focussing on finitely connected Erdös-Réyni graphs, Small-World Networks and Barabási-Albert scale-free networks. Results indicate that variability of input-output matrix elements, and random structures of the underlying graph tend to make the system less stable, while fast price dynamics or strong responsiveness to stock accumulation promote stability.     

Effects of agents' mobility on opinion spreading in Sznajd model

Under synchronous updating and allowing the agents to move in the lattice or underlying network, we find that the Sznajd model always reaches a consensus as a steady state, – because agent frustrations are removed due to their diffusion. Moreover, we succeed in obtaining the well-known phase transition of the traditional Sznajd model, which depends on the initial concentration of individuals following an opinion. How the time for reaching consensus depends on the system size, and on the topology have been exhaustively investigated. The analyzed topologies were: annealed and quenched dilution on a square lattice, as well as on a variant of the well-known Barabási-Albert model, called triad network.     

Memory effect in growing trees

We show that the structure of a growing tree preserves an information on the shape of an initial graph. For the exponential trees, evidence of this kind of memory is provided by means of the iterative equations, derived for the moments of the node–node distance distribution. Numerical calculations confirm the result and allow to extend the conclusion to the Barabási–Albert scale-free trees. The memory effect almost disappears, if subsequent nodes are connected to the network with more than one link.     

Risk Estimate of Diseases in Scale-Free Networks

We investigate the effect of risk estimate on the spread of diseases by the standard susceptible-infected- susceptible （SIS） model. The perception of the risk of being infected is explained as cutting off links among individuals, either healthy or infected, We study this simple dynamics on scale-free networks by analytical methods and computer simulations. We obtain the self-consistency form for the infection prevalence in steady states. For a given transmission rate, there exists a linear relationship between the reciprocal of the density of infected nodes and the estimate parameter. We confirm all the results by sufficient numerical simulations.     

Evolution of imitation networks in Minority Game model

The Minority Game is adapted to study the “imitation dilemma”, i.e. the tradeoff between local benefit and global harm coming from imitation. The agents are placed on a substrate network and are allowed to imitate more successful neighbours. Imitation domains, which are oriented trees, are formed. We investigate size distribution of the domains and in-degree distribution within the trees. We use four types of substrate: one-dimensional chain; Erd?s-Rényi graph; Barabási-Albert scale-free graph; Barabási-Albert 'model A' graph. The behaviour of some features of the imitation network strongly depend on the information cost epsilon, which is the percentage of gain the imitators must pay to the imitated. Generally, the system tends to form a few domains of equal size. However, positive epsilon makes the system stay in a long-lasting metastable state with complex structure. The in-degree distribution is found to follow a power law in two cases of those studied: for Erd?s-Rényi substrate for any epsilon and for Barabási-Albert scale-free substrate for large enough epsilon. A brief comparison with empirical data is provided.     

Influence of network structure on rumor propagation

Rumor propagation in complex networks is studied analytically and numerically by using the SIR model. Analytically, a mean-field theory is worked out by considering the influence of network topological structure and the unequal footings of neighbors of an infected node in propagating the rumor. It is found that the final infected density of population with degree k   is ρ(k)=1−exp(−αk)$\rho (k)=1-\exp (-\alpha k)$, where α is a parameter related to network structure. The number of the total final infected nodes depends on the network topological structure and will decrease when the structure changes from random to scale-free network. Numerical simulations confirm the theoretical predictions.     

Scale-Free Graph with Preferential Attachment and Evolving Internal Vertex Structure

We extend the classical Barabási-Albert preferential attachment procedure to graphs with internal vertex structure given by weights of vertices. In our model, weight dynamics depends on the current vertex degree distribution and the preferential attachment procedure takes into account both weights and degrees of vertices. We prove that such a coupled dynamics leads to scale-free graphs with exponents depending on parameters of the weight dynamics.     

Periodic Wave of Epidemic Spreading in Community Networks

It was reported by Cummings ef al. [Nature 427 （2004） 344] that there are periodic waves in the spatiotemporal data of epidemics. For understanding the mechanism, we study the epidemic spreading on community networks by both the SIS model and the SIRS model. We find that with the increase of infection rate, the number of total infected nodes may be stabilized at a fixed point, oscillatory waves, and periodic cycles. Moreover, the epidemic spreading in the SIS model can be explained by an analytic map.     

Comparison of immunization strategies in geographical networks

The epidemic spread and immunizations in geographically embedded scale-free (SF) and Watts-Strogatz (WS) networks are numerically investigated. We make a realistic assumption that it takes time which we call the detection time, for a vertex to be identified as infected, and implement two different immunization strategies: one is based on connection neighbors (CN) of the infected vertex with the exact information of the network structure utilized and the other is based on spatial neighbors (SN) with only geographical distances taken into account. We find that the decrease of the detection time is crucial for a successful immunization in general. Simulation results show that for both SF networks and WS networks, the SN strategy always performs better than the CN strategy, especially for more heterogeneous SF networks at long detection time. The observation is verified by checking the number of the infected nodes being immunized. We found that in geographical space, the distance preferences in the network construction process and the geographically decaying infection rate are key factors that make the SN immunization strategy outperforms the CN strategy. It indicates that even in the absence of the full knowledge of network connectivity we can still stop the epidemic spread efficiently only by using geographical information as in the SN strategy, which may have potential applications for preventing the real epidemic spread.     

Adsorption and Reaction of CO on （100） Surface of SrTiO3 by Density Function Theory Calculation

Adsorption and reaction of CO on two possible terminations of SrTiO3 （100） surface are investigated by the first-principles calculation of plane wave ultrasoft pseudopotentiai based on the density function theory. The adsorption energy, Mulliken population analysis, density of states （DOS） and electronic density difference of CO on SrTiO3 （100） surface, which have never been investigated before as far as we know are performed. The calculated results reveal that the Ti-CO orientation is the most stable configuration and the adsorption energy （0.449eV） is quite small. CO molecules adsorb weakly on the SrTiO3 （100） surface, there is predominantly electrostatic attraction between CO and the surface rather than a chemical bonding mechanism.     

Spatiotemporal Characteristic of Epidemic Spreading in Mobile Individuals

We numerical simulate the propagation behaviour and people distribution trait of epidemic spreading in mobile individuals by using cellular automaton method. The simulation results show that there exists a critical value of infected rate fluctuating amplitude, above which the epidemic can spread in whole population. Moreover, with the value of infected rate fluctuating amplitude increasing, the spatial distribution of infected population exhibits the spontaneous formation of irregular spiral waves and convergence phenomena, at the same time, the density of different populations will oscillate automatically with time. What is more, the traits of dynamic grow clearly and stably when the time and the value of infected rate fluctuating amplitude increasing. It is also found that the maximal proportion of infected individuals is independent of the value of fluctuating amplitude rate, but increases linearly with the population density.