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.     

社会群体中观点的信任、演化与共识

针对连续观点动力学模型中缺乏对个体信任及其观点的不同权重的考虑,本文通过扩展HegselmannKrause模型,引入个体间的信任度和观点间的相似度,将有限信任假设扩展为有限影响假设,建立带权重的观点更新模型,以研究社会群体中少数的偏执个体和权威个体对观点形成、演化以及共识构建过程的影响.仿真结果表明,这两类个体的初始观点尽量接近观点分布区间中点0.5或者增加偏执个体的影响阈值和权威个体的可信任程度可以使群体形成更少和更大的观点簇.随着偏执个体的影响阈值增加,最大簇的观点位置集中于0.5附近;而增加权威个体的可信任程度,最大簇的观点不断接近权威个体的最终观点.模型结果能够在一定程度上反映和解释现实社会中偏执个体和权威个体现象.     

Non-consensus Opinion Models on Complex Networks

Social dynamic opinion models have been widely studied to understand how interactions among individuals cause opinions to evolve. Most opinion models that utilize spin interaction models usually produce a consensus steady state in which only one opinion exists. Because in reality different opinions usually coexist, we focus on non-consensus opinion models in which above a certain threshold two opinions coexist in a stable relationship. We revisit and extend the non-consensus opinion (NCO) model introduced by Shao et al. (Phys. Rev. Lett. 103:01870, 2009). The NCO model in random networks displays a second order phase transition that belongs to regular mean field percolation and is characterized by the appearance (above a certain threshold) of a large spanning cluster of the minority opinion. We generalize the NCO model by adding a weight factor W to each individual’s original opinion when determining their future opinion (NCOW model). We find that as W increases the minority opinion holders tend to form stable clusters with a smaller initial minority fraction than in the NCO model. We also revisit another non-consensus opinion model based on the NCO model, the inflexible contrarian opinion (ICO) model (Li et al. in Phys. Rev. E 84:066101, 2011), which introduces inflexible contrarians to model the competition between two opinions in a steady state. Inflexible contrarians are individuals that never change their original opinion but may influence the opinions of others. To place the inflexible contrarians in the ICO model we use two different strategies, random placement and one in which high-degree nodes are targeted. The inflexible contrarians effectively decrease the size of the largest rival-opinion cluster in both strategies, but the effect is more pronounced under the targeted method. All of the above models have previously been explored in terms of a single network, but human communities are usually interconnected, not isolated. Because opinions propagate not only within single networks but also between networks, and because the rules of opinion formation within a network may differ from those between networks, we study here the opinion dynamics in coupled networks. Each network represents a social group or community and the interdependent links joining individuals from different networks may be social ties that are unusually strong, e.g., married couples. We apply the non-consensus opinion (NCO) rule on each individual network and the global majority rule on interdependent pairs such that two interdependent agents with different opinions will, due to the influence of mass media, follow the majority opinion of the entire population. The opinion interactions within each network and the interdependent links across networks interlace periodically until a steady state is reached. We find that the interdependent links effectively force the system from a second order phase transition, which is characteristic of the NCO model on a single network, to a hybrid phase transition, i.e., a mix of second-order and abrupt jump-like transitions that ultimately becomes, as we increase the percentage of interdependent agents, a pure abrupt transition. We conclude that for the NCO model on coupled networks, interactions through interdependent links could push the non-consensus opinion model to a consensus opinion model, which mimics the reality that increased mass communication causes people to hold opinions that are increasingly similar. We also find that the effect of interdependent links is more pronounced in interdependent scale free networks than in interdependent Erd?s Rényi networks.     

Evolutionary fate of memory-one strategies in repeated prisoner’s dilemma game in structured populations

We study evolutionary spatial prisoner’s dilemma game involving a one-step memory mechanism of the individuals whenever making strategy updating. In particular, during the process of strategy updating, each individual keeps in mind all the outcome of the action pairs adopted by himself and each of his neighbors in the last interaction, and according to which the individuals decide what actions they will take in the next round. Computer simulation results imply that win-stay-lose-shift like strategy win out of the memory-one strategy set in the stationary state. This result is robust in a large range of the payoff parameter, and does not depend on the initial state of the system. Furthermore, theoretical analysis with mean field and quasi-static approximation predict the same result. Thus, our studies suggest that win-stay-lose-shift like strategy is a stable dominant strategy in repeated prisoner’s dilemma game in homogeneous structured populations.     

Computational Power of Asynchronously Tuned Automata Enhancing the Unfolded Edge of Chaos

Asynchronously tuned elementary cellular automata (AT-ECA) are described with respect to the relationship between active and passive updating, and that spells out the relationship between synchronous and asynchronous updating. Mutual tuning between synchronous and asynchronous updating can be interpreted as the model for dissipative structure, and that can reveal the critical property in the phase transition from order to chaos. Since asynchronous tuning easily makes behavior at the edge of chaos, the property of AT-ECA is called the unfolded edge of chaos. The computational power of AT-ECA is evaluated by the quantitative measure of computational universality and efficiency. It shows that the computational efficiency of AT-ECA is much higher than that of synchronous ECA and asynchronous ECA.     

Diversity of contribution promotes cooperation in public goods games

In most previous studies of public goods game, individuals conventionally donate their contributions equally to the games they participate in. We develop an extended public goods game model, in which individuals distribute their contributions based on the groups’ qualities. Namely, the individuals are allowed to increase their investment to the superior groups at the expense of the nasty ones. The quality of a group is positively correlated with its cooperation level. In numerical simulations, synchronized stochastic strategy updating rule based on pairwise comparison for a fixed noise level is adopted. The results show that the high-quality group preference mechanism can greatly improve cooperation, compared with conventional models. Besides, the system with stronger preference toward high-quality groups performs better. Investigation of wealth distribution at equilibrium reveals that cooperators’ wealth appreciates with the increase of preference degree when cooperators take up the same fraction of the population.     

Cellular automaton models of driven diffusive Frenkel-Kontorova-type systems

Three cellular automaton models of increasing complexity are introduced to model driven diffusive systems related to the generalized Frenkel-Kontorova (FK) models recently proposed by Braun et al. [Phys. Rev. E 58, 1311 (1998)]. The models are defined in terms of parallel updating rules. Simulation results are presented for these models. The features are qualitatively similar to those models defined previously in terms of sequentially updating rules. Essential features of the FK model such as phase transitions, jamming due to atoms in the immobile state, and hysteresis in the relationship between the fraction of atoms in the running state and the bias field are captured. Formulating in terms of parallel updating rules has the advantage that the models can be treated analytically by following the time evolution of the occupation on every site of the lattice. Results of this analytical approach are given for the two simpler models. The steady state properties are found by studying the stable fixed points of a closed set of dynamical equations obtained within the approximation of retaining spatial correlations only up to two nearest-neighboring sites. Results are found to be in good agreement with numerical data.     

Decision Accuracy and the Role of Spatial Interaction in Opinion Dynamics

The opinions and actions of individuals within interacting groups are frequently determined by both social and personal information. When sociality (or the pressure to conform) is strong and individual preferences are weak, groups will remain cohesive until a consensus decision is reached. When group decisions are subject to a bias, representing for example private information known by some members of the population or imperfect information known by all, then the accuracy achieved for a fixed level of bias will increase with population size. In this work we determine how the scaling between accuracy and group size can be related to the microscopic properties of the decision-making process. By simulating a spatial model of opinion dynamics we show that the relationship between the instantaneous fraction of leaders in the population (L), system size (N), and accuracy depends on the frequency of individual opinion switches and the level of population viscosity. When social mixing is slow, and individual opinion changes are frequent, accuracy is determined by the absolute number of informed individuals. As mixing rates increase, or the rate of opinion updates decrease, a transition occurs to a regime where accuracy is determined by the value of $L\sqrt{ N}$ . We investigate the transition between different scaling regimes analytically by examining a well-mixed limit.     

The noisy Hegselmann-Krause model for opinion dynamics

In the model for continuous opinion dynamics introduced by Hegselmann and Krause, each individual moves to the average opinion of all individuals within an area of confidence. In this work we study the effects of noise in this system. With certain probability, individuals are given the opportunity to change spontaneously their opinion to another one selected randomly inside the opinion space with different rules. If the random jump does not occur, individuals interact through the Hegselmann-Krause’s rule. We analyze two cases, one where individuals can carry out opinion random jumps inside the whole opinion space, and other where they are allowed to perform jumps just inside a small interval centered around the current opinion. We found that these opinion random jumps change the model behavior inducing interesting phenomena. Using pattern formation techniques, we obtain approximate analytical results for critical conditions of opinion cluster formation. Finally, we compare the results of this work with the noisy version of the Deffuant et al. model [G. Deffuant, D. Neu, F. Amblard, G. Weisbuch, Adv. Compl. Syst. 3, 87 (2000)] for continuous-opinion dynamics.     

嵌入式软件在线升级系统的设计与实现

对嵌入式软件在线升级有利于维持系统的稳定性,可实现在线测试,支持系统在线重构,是提高系统可靠性的有效途径。对嵌入式软件的在线升级进行了研究,研究了在线升级的颗粒度和升级点的选择,分析了程序状态的识别和恢复,提出了采用动态分析与静态分析相结合的方法保证升级的安全的方法,实现了在线升级方案。基于在线升级方案构建嵌入式软件系统,实现了应用系统软件的模块级粒度的升级。最后基于在线升级系统设计实现了小卫星星务管理软件,具备了灵活的在线升级能力,表明在线升级系统具有很好的工程实用价值。     

Two-cycles in spin-systems: sequential versus synchronous updating in multi-state Ising-type ferromagnets

Hamiltonians for general multi-state spin-glass systems with Ising symmetry are derived for both sequential and synchronous updating of the spins. The possibly different behaviour caused by the way of updating is studied in detail for the (anti)-ferromagnetic version of the models, which can be solved analytically without any approximation, both thermodynamically via a free-energy calculation and dynamically using the generating functional approach. Phase diagrams are discussed and the appearance of two-cycles in the case of synchronous updating is examined. A comparative study is made for the Q-Ising and the Blume-Emery-Griffiths ferromagnets and some interesting physical differences are found. Numerical simulations confirm the results obtained.Received: 9 August 2004, PACS: 05.70.Fh Phase transitions: general studies - 64.60.Cn Order-disorder transformations; statistical mechanics of model systems - 75.10.Hk Classical spin models     

Ising model on evolution networks and its application on opinion formation

Many phenomena show that in a favorable circumstance an agent still has an updating possibility, and in an unfavor- able circumstance an agent also has a possibility of holding its own state and reselecting its neighbors. To describe this kind of phenomena an Ising model on evolution networks was presented and used for consensus formation and separation of opinion groups in human population. In this model the state-holding probability p and selection-rewiring probability q were introduced. The influence of this mixed dynamics of spin flips and network rewiring on the ordering behavior of the model was investigated, p hinders ordering of opinion networks and q accelerates the dynamical process of networks. Influence of q on the ordering and separating stems from its effect on average path length of networks.     

EMR对混沌同步保密通信系统干扰的初步研究

 使用GTEM Cell实验系统,研究了连续波电磁辐射对基于混沌同步理论的保密通信系统的电磁干扰。混沌保密通信系统采用由典型的Chua氏混沌电路构造混沌同步系统,采用掩盖法对模拟信号进行加密传输。实验发现：在100MHz~150MHz的频率范围内,超过一定功率密度的电磁辐射会导致系统的混沌加密功能失效,此后即使停止电磁辐射,系统仍无法自行恢复到混沌加密状态。     

Toom’s Model with Glauber Rates: An Exact Solution Using Elementary Methods

A simple spatially two-dimensional stochastic cellular automaton with asymmetric coupling and synchronous updating according to Glauber rates is considered. While detailed balance is violated it is still possible to compute analytically the stationary probability distribution by elementary means. The stationary distribution can be written as a canonical equilibrium distribution of a spin system on a triangular lattice with nearest neighbour coupling. Thus, the cellular automaton shows a nonequilibrium phase transition with Ising critical behaviour.     

Fitness of others' evaluation effect promotes cooperation in spatial public goods game

Payoff-driven strategy updating rule has always been adopted as a classic mechanism, but up to now, there have been a great many of researches on considering other forms of strategy updating rules, among which pursuing high fitness is one of the most direct and conventional motivations in the decision-making using game theory. But there are few or no researches on fitness from the perspective of others' evaluation. In view of this, we propose a new model in which the evaluation effect with fitness-driven strategy updating rule is taken into consideration, and introduce an evaluation coefficient to present the degree of others' evaluation on individual's behavior. The cooperative individuals can get positive evaluation, otherwise defective individuals get negative evaluation, and the degree of evaluation is related to the number of neighbors who have the same strategy of individual. Through numerical simulation, we find that the evaluation effect of others can enhance the network reciprocity, thus promoting the cooperation. For a strong dilemma, the higher evaluation coefficient can greatly weaken the cooperation dilemma; for a weak one, the higher evaluation coefficient can make cooperator clusters spread faster, however, there is no significant difference in the level of cooperation in the final stable state among different evaluation coefficients. The cooperation becomes more flourish as the number of fitness-driven individuals increases, when all individuals adopt fitness-driven strategy updating rule, the cooperators can quickly occupy the whole population. Besides, we demonstrate the robustness of the results on the WS small-world network, ER random network, and BA scale-free network.     

Factorised steady states and condensation transitions in nonequilibrium systems

Systems driven out of equilibrium can often exhibit behaviour not seen in systems in thermal equilibrium —for example phase transitions in one-dimensional systems. In this talk I will review a simple model of a nonequilibrium system known as the ‘zero-range process’ and its recent developments. The nonequilibrium stationary state of this model factorises and this property allows a detailed analysis of several ‘condensation’ transitions wherein a finite fraction of the constituent particles condenses onto a single lattice site. I will then consider a more general class of mass transport models, encompassing continuous mass variables and discrete time updating, and present a necessary and sufficient condition for the steady state to factorise. The property of factorisation again allows an analysis of the condensation transitions which may occur.     

Effects of Inertia on Evolutionary Prisoner's Dilemma Game

Considering the inertia of individuals in real life, we propose a modified Fermi updating rule, where the inertia of players is introduced into evolutionary prisoner's dilemma game (PDG) on square lattices. We mainly focus on how the inertia affects the cooperative behavior of the system. Interestingly, we find that the cooperation level has a nonmonotonic dependence on the inertia: with small inertia, cooperators will soon be invaded by defectors; with large inertia, players are unwilling to change their strategies and the cooperation level remains the same as the initial state; while a moderate inertia can induce the highest cooperation level. Moreover, effects of environmental noise and individual inertia are studied. Our work may be helpful in understanding the emergence and persistence of cooperation in nature and society.     

Opinion Polarization in Human Communities Can Emerge as a Natural Consequence of Beliefs Being Interrelated

The emergence of opinion polarization within human communities—the phenomenon that individuals within a society tend to develop conflicting attitudes related to the greatest diversity of topics—has been a focus of interest for decades, both from theoretical and modelling points of view. Regarding modelling attempts, an entire scientific field—opinion dynamics—has emerged in order to study this and related phenomena. Within this framework, agents’ opinions are usually represented by a scalar value which undergoes modification due to interaction with other agents. Under certain conditions, these models are able to reproduce polarization—a state increasingly familiar to our everyday experience. In the present paper, an alternative explanation is suggested along with its corresponding model. More specifically, we demonstrate that by incorporating the following two well-known human characteristics into the representation of agents: (1) in the human brain beliefs are interconnected, and (2) people strive to maintain a coherent belief system; polarization immediately occurs under exposure to news and information. Furthermore, the model accounts for the proliferation of fake news, and shows how opinion polarization is related to various cognitive biases.     

Effects of Inertia on Evolutionary Prisoner's Dilemma Game

Considering the inertia of individuals in real life,we propose a modified Fermi updating rule,where the inertia of players is introduced into evolutionary prisoner's dilemma game(PDG) on square lattices.We mainly focus on how the inertia affects the cooperative behavior of the system.Interestingly,we find that the cooperation level has a nonmonotonic dependence on the inertia:with small inertia,cooperators will soon be invaded by defectors;with large inertia,players are unwilling to change their strategies and the cooperation level remains the same as the initial state;while a moderate inertia can induce the highest cooperation level.Moreover,effects of environmental noise and individual inertia are studied.Our work may be helpful in understanding the emergence and persistence of cooperation in nature and society.     

用双稳态势场模型研究观点转变的驱动-响应关系

从物理学的视角看,群体观点演化实质可以看作是观点粒子状态变化的集体效应.本文考察在双稳态势中噪声诱导观点粒子的状态转变,利用加权拉盖尔完备正交函数法计算了时间关联函数和描述驱动-响应关系的弛豫时间.理论计算结果表明,噪声诱导作用存在一个临界值Dc,若噪声强度高于临界值,时间关联函数随关联时间呈指数型增加.结果还显示,存在弛豫时间随势垒纵横比/噪声强度变化取值趋于无穷的双奇异点现象.奇异点处无法实现观点粒子状态的转变.弛豫时间与势垒纵横比之间存在线性关系,预示着在双稳态势场中观点粒子受噪声驱动呈现类似牛顿第二定律的驱动-响应关系,而弛豫时间在这个关系中充当表征惯性质量的角色.