Robustness of critical points in a complex adaptive system: Effects of hedge behavior

In our recent papers, we have identified a class of phase transitions in the market-directed resource-allocation game, and found that there exists a critical point at which the phase transitions occur. The critical point is given by a certain resource ratio. Here, by performing computer simulations and theoretical analysis, we report that the critical point is robust against various kinds of human hedge behavior where the numbers of herds and contrarians can be varied widely. This means that the critical point can be independent of the total number of participants composed of normal agents, herds and contrarians, under some conditions. This finding means that the critical points we identified in this complex adaptive system (with adaptive agents) may also be an intensive quantity, similar to those revealed in traditional physical systems (with non-adaptive units).     

Agreement dynamics on interaction networks with diverse topologies

We review the behavior of a recently introduced model of agreement dynamics, called the "Naming Game." This model describes the self-organized emergence of linguistic conventions and the establishment of simple communication systems in a population of agents with pairwise local interactions. The mechanisms of convergence towards agreement strongly depend on the network of possible interactions between the agents. In particular, the mean-field case in which all agents communicate with all the others is not efficient, since a large temporary memory is requested for the agents. On the other hand, regular lattice topologies lead to a fast local convergence but to a slow global dynamics similar to coarsening phenomena. The embedding of the agents in a small-world network represents an interesting tradeoff: a local consensus is easily reached, while the long-range links allow to bypass coarsening-like convergence. We also consider alternative adaptive strategies which can lead to faster global convergence.     

Rescaled Range Permutation Entropy: A Method for Quantifying the Dynamical Complexity of Extreme Volatility in Chaotic Time Series

Information entropy,as a quantitative measure of complexity in nonlinear systems,has been widely researched in a variety of contexts.With the development of a nonlinear dynamic,the entropy is faced with severe challenges in dealing with those signals exhibiting extreme volatility.In order to address this problem of weighted permutation entropy,which may result in the inaccurate estimation of extreme volatility,we propose a rescaled range permutation entropy,which selects the ratio of range and standard deviation as the weight of different fragments in the time series,thereby effectively extracting the maximum volatility.By analyzing typical nonlinear systems,we investigate the sensitivities of four methods in chaotic time series where extreme volatility occurs.Compared with sample entropy,fuzzy entropy,and weighted permutation entropy,this rescaled range permutation entropy leads to a significant discernibility,which provides a new method for distinguishing the complexity of nonlinear systems with extreme volatility.     

Statistical physics of human beings in games:Controlled experiments

It is important to know whether the laws or phenomena in statistical physics for natural systems with non-adaptive agents still hold for social human systems with adaptive agents, because this implies whether it is possible to study or understand social human systems by using statistical physics originating from natural systems. For this purpose, we review the role of human adaptability in four kinds of specific human behaviors, namely, normal behavior, herd behavior, contrarian behavior, and hedge behavior. The approach is based on controlled experiments in the framework of market-directed resource-allocation games. The role of the controlled experiments could be at least two-fold: adopting the real human decision-making process so that the system under consideration could reflect the performance of genuine human beings;making it possible to obtain macroscopic physical properties of a human system by tuning a particular factor of the system,thus directly revealing cause and effect. As a result, both computer simulations and theoretical analyses help to show a few counterparts of some laws or phenomena in statistical physics for social human systems: two-phase phenomena or phase transitions, entropy-related phenomena, and a non-equilibrium steady state. This review highlights the role of human adaptability in these counterparts, and makes it possible to study or understand some particular social human systems by means of statistical physics coming from natural systems.     

Adaptive cyclically dominating game on co-evolving networks: numerical and analytic results

A co-evolving and adaptive Rock (R)–Paper (P)–Scissors (S) game (ARPS) in which an agent uses one of three cyclically dominating strategies is proposed and studied numerically and analytically. An agent takes adaptive actions to achieve a neighborhood to his advantage by rewiring a dissatisfying link with a probability p or switching strategy with a probability 1 - p. Numerical results revealed two phases in the steady state. An active phase for p < p _c has one connected network of agents using different strategies who are continually interacting and taking adaptive actions. A frozen phase for p > p _c has three separate clusters of agents using only R, P, and S, respectively with terminated adaptive actions. A mean-field theory based on the link densities in co-evolving network is formulated and the trinomial closure scheme is applied to obtain analytical solutions. The analytic results agree with simulation results on ARPS well. In addition, the different probabilities of winning, losing, and drawing a game among the agents are identified as the origin of the small discrepancy between analytic and simulation results. As a result of the adaptive actions, agents of higher degrees are often those being taken advantage of. Agents with a smaller (larger) degree than the mean degree have a higher (smaller) probability of winning than losing. The results are informative for future attempts on formulating more accurate theories.     

Self-organized cooperative behavior and critical penalty in an evolving population

The emergence of cooperation and the effectiveness of penalties among competing agents are studied via a model of evolutionary game incorporating adaptive behavior and penalties for illegal acts. For initially identical agents, a phase diagram is obtained via an analytic approach, with results in good agreement with numerical simulations. The results show that there exists a critical penalty for achieving a completely honest population and a sufficiently well-behaved initial population requires no penalty. Self-organized segregation to extreme actions emerges in the dynamics for a system with uniformly distributed initial tendencies for cooperation. After training, the penalty can be relaxed without ruining the adapted cooperative behavior. Results of our model in a population taking on the form of a 2D square lattice are also reported.     

Exact solution of a modified El Farol's bar problem: Efficiency and the role of market impact

We discuss a model of heterogeneous, inductive rational agents inspired by the El Farol Bar problem and the Minority Game. As in markets, agents interact through a collective aggregate variable — which plays a role similar to price — whose value is fixed by all of them. Agents follow a simple reinforcement-learning dynamics where the reinforcement, for each of their available strategies, is related to the payoff delivered by that strategy. We derive the exact solution of the model in the “thermodynamic” limit of infinitely many agents using tools of statistical physics of disordered systems. Our results show that the impact of agents on the market price plays a key role: even though price has a weak dependence on the behavior of each individual agent, the collective behavior crucially depends on whether agents account for such dependence or not. Remarkably, if the adaptive behavior of agents accounts even “infinitesimally” for this dependence they can, in a whole range of parameters, reduce global fluctuations by a finite amount. Both global efficiency and individual utility improve with respect to a “price taker” behavior if agents account for their market impact.     

自适应光学中的非等晕性

本文讨论了自适应光学中非等晕域对补偿效果的影响,提出了一种减小非等晕性误差的新方法—位相梯度法。分析结果表明,该方法可显著增大有效校正的角范围,使非等晕性误差的影响大大减小。我们预期位相梯度法有望解决自适应光学中信标的非等晕性问题。     

Evolution of cooperation among mobile agents with heterogenous view radii

In this paper, we study cooperative behavior among mobile agents; the agents have heterogenous view radii and they play the prisoner’s dilemma game with those being within their vision fields. It is found that the cooperation level is remarkably promoted when the heterogeneity of view radii is considered, and the degree distribution of the system is investigated to explain this interesting phenomenon. Moreover, we report that the cooperative behavior is best favored by low density, moderate view radius, and small moving speed. Our findings may be helpful in understanding cooperative behavior in natural and social systems consisting of mobile agents.     

Low-frequency noise controls on-off intermittency of bifurcating systems

A bifurcating system subject to multiplicative noise can display on-off intermittency. Using a canonical example, we investigate the extreme sensitivity of the intermittent behavior to the nature of the noise. Through a perturbative expansion and numerical studies of the probability density function of the unstable mode, we show that intermittency is controlled by the ratio between the departure from onset and the value of the noise spectrum at zero frequency. Reducing the noise spectrum at zero frequency shrinks the intermittency regime drastically. This effect also modifies the distribution of the duration that the system spends in the off phase. Mechanisms and applications to more complex bifurcating systems are discussed.     

Variations of trends of indicators describing complex systems: change of scaling precursory to extreme events

Socioeconomic and natural complex systems persistently generate extreme events also known as disasters, crises, or critical transitions. Here we analyze patterns of background activity preceding extreme events in four complex systems: economic recessions, surges in homicides in a megacity, magnetic storms, and strong earthquakes. We use as a starting point the indicators describing the system's behavior and identify changes in an indicator's trend. Those changes constitute our background events (BEs). We demonstrate a premonitory pattern common to all four systems considered: relatively large magnitude BEs become more frequent before extreme event. A premonitory change of scaling has been found in various models and observations. Here we demonstrate this change in scaling of uniformly defined BEs in four real complex systems, their enormous differences notwithstanding.     

Dynamics of self-organization in complex adaptive networks

We study the dynamical behavior of complex adaptive automata during unsupervised learning of periodic training sets. A new technique for their analysis is presented and applied to an adaptive network with distributed memory. We show that with general imput pattern sequences, the system can display behavior that ranges from convergence into simple fixed points and oscillations to chaotic wanderings. We also test the ability of the self-organized automaton to recognize spatial patterns, discriminate between them, and to elicit meaningful information out of noisy inputs. In this configuration we determine that the higher the ratio of excitation to inhibition, the broader the equivalence class into which patterns are put together.     

An approach to chaotic synchronization

This paper deals with the chaotic oscillator synchronization. An approach to the synchronization of chaotic oscillators has been proposed. This approach is based on the analysis of different time scales in the time series generated by the coupled chaotic oscillators. It has been shown that complete synchronization, phase synchronization, lag synchronization, and generalized synchronization are the particular cases of the synchronized behavior called "time-scale synchronization." The quantitative measure of chaotic oscillator synchronous behavior has been proposed. This approach has been applied for the coupled R?ssler systems and two coupled Chua's circuits.     

微矩形凹槽表面液滴各向异性浸润行为的研究

受自然界启发,仿生微结构被广泛用于调控固-液界面的性质.研究显示,液滴在微结构表面的各向异性浸润行为可用于实现微流动方向和速度的控制,且其各向异性浸润与微结构的尺寸和分布等密切相关.本文研究了微矩形凹槽尺寸对液滴各向异性浸润行为的影响规律.结果显示,液滴沿平行沟槽的方向具有较小的运动阻力、易铺展,因此具有较小接触角;而垂直于沟槽方向,由于沟槽的阻隔作用具有较大运动阻力,因而具有较大接触角,并且在垂直方向液滴的浸润过程是三相线一系列钉扎和跳跃行为.在微矩形凹槽表面,液滴沿平行方向接触角θ//与肋板宽度R和凹槽宽度G密切相关,其值与表面固体面积比成反比;而垂直于沟槽方向的接触角θ⊥随肋板宽度R和凹槽宽度G变化基本保持不变.同时各向异性液滴的变形比L/W、特征方向接触角比值θ⊥/θ//与表面固体面积比成正比.研究结果有助于加深理解微结构表面浸润行为的机制,并为微矩形凹槽在微流动控制方向的应用提供技术支持.     

Towards classification of the bifurcation structure of a spherical cavitation bubble

We focus on a single cavitation bubble driven by ultrasound, a system which is a specimen of forced nonlinear oscillators and is characterized by its extreme sensitivity to the initial conditions. The driven radial oscillations of the bubble are considered to be implicated by the principles of chaos physics and owing to specific ranges of control parameters, can be periodic or chaotic. Despite the growing number of investigations on its dynamics, there is not yet an inclusive yardstick to sort the dynamical behavior of the bubble into classes; also, the response oscillations are so complex that long term prediction on the behavior becomes difficult to accomplish. In this study, the nonlinear dynamics of a bubble oscillator was treated numerically and the simulations were proceeded with bifurcation diagrams. The calculated bifurcation diagrams were compared in an attempt to classify the bubble dynamic characteristics when varying the control parameters. The comparison reveals distinctive bifurcation patterns as a consequence of driving the systems with unequal ratios of (where R₀ is the bubble initial radius and λ is the wavelength of the driving ultrasonic wave). Results indicated that systems having the equal ratio of , share remarkable similarities in their bifurcating behavior and can be classified under a unit category.