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Consensus of population systems with community structures

Physical Review E 2008年第5期78卷 051923-051923页

作者： Jing Wang Bin Wu Long Wang Feng Fu Center for Systems and Control State Key Laboratory for Turbulence and Complex Systems College of Engineering Peking University Beijing 100871 China Program for Evolutionary Dynamics Harvard University One Brattle Square Cambridge Massachusetts 02138 USA

Multicommunity population systems may reach a consensus state where the fractions of each species in different communities agree on a common value. In this paper, by analyzing the evolutionary dynamics based on an extended replicator equation incorporating community effects, the consensus problem of population systems with n communities is studied. In particular, the simple case of two communities is investigated in detail. In general, for n communities, a sufficient and necessary condition for population systems to reach a consensus of coexistent state is provided. Regarding the population dynamics for the four different types of games, whether the population systems can achieve consensus is determined. The dynamics of community-structured populations shows richer features than nonstructured populations, and some nontrivial phenomena arising from different community-structured population systems are illustrated with concrete numerical examples.

关键词： Population dynamics

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Effects of heterogeneous wealth distribution on public cooperation with collective risk

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Physical Review E 2010年第1期82卷 016102-016102页

作者： Jing Wang Feng Fu Long Wang Center for Systems and Control State Key Laboratory for Turbulence and Complex Systems College of Engineering Peking University Beijing 100871 China Program for Evolutionary Dynamics Harvard University One Brattle Square Cambridge Massachusetts 02138 USA

The distribution of wealth among individuals in real society can be well described by the Pareto principle or “80-20 rule.” How does such heterogeneity in initial wealth distribution affect the emergence of public cooperation, when individuals, the rich and the poor, engage in a collective-risk enterprise, not to gain a profit but to avoid a potential loss? Here we address this issue by studying a simple but effective model based on threshold public goods games. We analyze the evolutionary dynamics for two distinct scenarios, respectively: one with fair sharers versus defectors and the other with altruists versus defectors. For both scenarios, particularly, we in detail study the dynamics of the population with dichotomic initial wealth—the rich versus the poor. Moreover, we demonstrate the possible steady compositions of the population and provide the conditions for stability of these steady states. We prove that in a population with heterogeneous wealth distribution, richer individuals are more likely to cooperate than poorer ones. Participants with lower initial wealth may choose to cooperate only if all players richer than them are cooperators. The emergence of pubic cooperation largely relies on rich individuals. Furthermore, whenever the wealth gap between the rich and the poor is sufficiently large, cooperation of a few rich individuals can substantially elevate the overall level of social cooperation, which is in line with the well-known Pareto principle. Our work may offer an insight into the emergence of cooperative behavior in real social situations where heterogeneous distribution of wealth among individual is omnipresent.

关键词： Pareto principle

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Iteration complexity analysis of a partial LQP-based alternating direction method of multipliers

arXiv

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arXiv 2021年

作者： Bai, Jianchao Ma, Yuxue Sun, Hao Zhang, Miao School of Mathematics and Statistics MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710129 China Department of Mathematics Louisiana State University Baton RougeLA70803-4918 United States

In this paper, we consider a prototypical convex optimization problem with multi-block variables and separable structures. By adding the Logarithmic Quadratic Proximal (LQP) regularizer with suitable proximal parameter to each of the first grouped subproblems, we develop a partial LQP-based Alternating Direction Method of Multipliers (ADMM-LQP). The dual variable is updated twice with relatively larger stepsizes than the classical region (0, 1+√5). Using a prediction-correction approach to analyze properties of the iterates 2 generated by ADMM-LQP, we establish its global convergence and sublinear convergence rate of O(1/T) in the new ergodic and nonergodic senses, where T denotes the iteration index. We also extend the algorithm to a nonsmooth composite convex optimization and establish similar convergence results as our ADMM-LQP. © 2021, CC BY.

关键词： Convex optimization

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Shapiro steps and chaos in the Frenkel-Kontorova model with substrate lateral vibration

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Physical Review E 2022年第4期106卷 044204-044204页

作者： Yongfeng Wei Youming Lei School of Mathematics and Statistics Northwestern Polytechnical University Xi'an 710072 China Ministry of Industry and Information Technology Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'an 710072 China

Numerical simulations are used to examine the dynamics of the dc-driven Frenkel-Kontorova model with an oscillation substrate subjected to lateral periodic excitations in overdamped and underdamped cases, respectively. The results reveal that the system exhibits frequency locking and chaotic behaviors due to the fact that the lateral vibration of the substrate potential introduces an additional frequency and degree of freedom into the system. In the overdamped case, we show that the appearance of subharmonic Shapiro steps can be attributed to the deformation of the substrate potential or inertia. The characteristics of the steps are significantly affected by the amplitude and frequency of the lateral vibration. When the vibration frequency is relatively high, the change of the width of the first harmonic Shapiro step with increasing amplitude exhibits a Bessel-type oscillation, but the oscillation deviates from the Bessel curve at lower frequencies. In the amplitude dependence, although the oscillatory behavior of the critical depinning force at the high frequency is anomalous, local maxima (minima) of the first step width correspond to local minima (maxima) of the critical depinning force, and the largest Lyapunov exponent obtained in the pinned state represents a mirror relationship of the critical depinning force. In contrast to the overdamped system, the underdamped one exhibits both subharmonic Shapiro steps and chaotic behaviors. We show the increased inertia of the latter system plays an important role in suppressing the emergence of subharmonic steps, which is opposite to the result of the former. When the dc force changes, chaos appears not only between adjacent subharmonic Shapiro steps but also on some specific steps where chaos should be avoided. The variation regularity of the first step width and the critical depinning force is thus annihilated in vibration amplitude and frequency dependence. However, superlubricity can be achieved by careful adjustmen

关键词： Chaos Classical mechanics Coupled oscillators Synchronization

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热-电-弹压电/石墨烯复合纳米板在粘弹性地基上的非线性受迫振动

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Acta Mechanica Sinica 2023年第3期39卷 142-152页

作者：赵云平侯秀慧张硕孙彤彤都琳邓子辰 Department of Applied Mathematics Northwestern Polytechnical UniversityXi'an 710072China Deparment of Engineering Mechanics Northwestern Polytechnical University Xi'an 710072China Ministry of Industry and Information Technology Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical UniversityXi'an 710072China

本文研究了非对称压电/石墨烯复合纳米板在粘弹性地基上、热环境及外部简谐激励作用下的动力学行为.根据Hamilton原理和Kirchhoff板理论,建立复合纳米板的动力学方程,并通过Galerkin方法对简支边界下的动力学方程进行求解,获得了一个包... 详细信息

本文研究了非对称压电/石墨烯复合纳米板在粘弹性地基上、热环境及外部简谐激励作用下的动力学行为.根据Hamilton原理和Kirchhoff板理论,建立复合纳米板的动力学方程,并通过Galerkin方法对简支边界下的动力学方程进行求解,获得了一个包含有二次非线性项的Duffing-Helmholtz方程.从解析和数值方面分别分析了非局部弹性参数、温度、粘弹性基体、电压以及纳米板的几何尺寸对系统非线性与线性频率比和非线性振动行为的影响.此外,本文揭示了系统的非对称性和二次非线性项之间的对应关系.本研究的动力学结果将为压电-石墨烯复合纳米谐振器力学性能的实验表征提供理论依据.

关键词： Asymmetric piezoelectric-graphene composite nanoplate Thermal environment Nonlinear forced vibration Wave number

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Entropic stochastic resonance of finite-size particles in confined Brownian transport

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Physical Review E 2024年第5期109卷 054110-054110页

作者： Hai-Wei Hu Lin Du Ai-Li Fan Zi-Chen Deng Celso Grebogi School of Mathematics and Statistics Northwestern Polytechnical University Xi'an 710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'an 710072 China School of Aeronautics Northwestern Polytechnical University Xi'an 710072 China Institute for Complex Systems and Mathematical Biology Kingdom College University of Aberdeen Aberdeen AB24 3UE United Kingdom

We demonstrate the existence of entropic stochastic resonance (ESR) of passive Brownian particles with finite size in a double- or triple-circular confined cavity, and compare the similarities and differences of ESR in the double-circular cavity and triple-circular cavity. When the diffusion of Brownian particles is constrained to the double- or triple-circular cavity, the presence of irregular boundaries leads to entropic barriers. The interplay between the entropic barriers, a periodic input signal, the gravity of particles, and intrinsic thermal noise may give rise to a peak in the spectral amplification factor and therefore to the appearance of the ESR phenomenon. It is shown that ESR can occur in both a double-circular cavity and a triple-circular cavity, and by adjusting some parameters of the system, the response of the system can be optimized. The differences are that the spectral amplification factor in a triple-circular cavity is significantly larger than that in a double-circular cavity, and compared with the ESR in a double-circular cavity, the ESR effect in a triple-circular cavity occurs within a wider range of external force parameters. In addition, the strength of ESR also depends on the particle radius, and smaller particles can induce more obvious ESR, indicating that the size effect cannot be safely neglected. The ESR phenomenon usually occurs in small-scale systems where confinement and noise play an important role. Therefore, the mechanism that is found could be used to manipulate and control nanodevices and biomolecules.

关键词： Brownian motion Stochastic dynamical systems Brownian dynamics Fokker–Planck equation Langevin equation

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Transport and escape in a deformable channel driven by fractional Gaussian noise

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Physical Review E 2019年第2期100卷 022114-022114页

作者： Ruoxing Mei Yong Xu Jürgen Kurths Department of Applied Mathematics Northwestern Polytechnical University Xi'an 710072 China Department of Applied Mathematics Northwestern Polytechnical University Xi'an 710072 China and MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'an 710072 China Potsdam Institute for Climate Impact Research Potsdam 14412 Germany

Fractional Gaussian noise (FGN) with the Hurst exponent H is an important tool to model various phenomena in biophysical systems, like subdiffusion in a single protein molecule. Considering that there also exists a confined structure which can be modeled as a channel in these systems, transport and escape driven by FGN in a deformable channel are investigated in this paper. By calculating the mean velocity, and the mean first passage time (MFPT) for crossing the nearest bottleneck and the probability distribution of the final position, effects of FGN and channel structure on the system dynamics are illustrated. Our results indicate that FGN has a complex influence mechanism under different combinations of H and the noise intensity. For a persistence case (H>0.5), the mean velocity decreases but MFPT increases with the increase of the noise intensity and H. While for an antipersistence case (H<0.5), when H is small, the relationships among the mean velocity, MFPT and the noise intensity are exactly the opposite to persistence cases. When H has a large value, the mean velocity tends to first decrease and then increase. Moreover, effects of the bottleneck and channel asymmetry are investigated. It is shown that a small H and a large channel width can lead to a large mean velocity and fast crossing. Besides, a channel asymmetry can affect the system dynamics by inducing asymmetric structure and adjusting the width of bottleneck. However, the effect of the bottleneck is the main factor. Therefore, a combination of channel with wide bottleneck and FGN in an antipersistence regime is the optimal choice to promote the transport and escape. These results provide a basis for the explanation of molecular activity in living organisms and the design of particle mixture separators.

关键词： Noise Particle phenomena Transport phenomena

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Residual-Based Multi-peak Sampling Algorithm in Inverse Problems of Dynamical systems

arXiv

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arXiv 2023年

作者： An, Xiao-Kai Du, Lin Deng, Zi-Chen Zhang, Yu-Jia Miit Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'An710072 China School of Mathematics and Statistics Northwestern Polytechnical University Xi'An710072 China School of Aeronautics Northwestern Polytechnical University Xi'An710072 China

Stochastic differential equations can describe a wide range of dynamical systems, and obtaining the governing equations of these systems is the premise of studying the nonlinear dynamic behavior of the system. Neural networks are currently the most popular approach in the inverse problem of dynamical systems. In order to obtain accurate dynamical equations, neural networks need a large amount of trajectory data as a training set. To address this shortcoming, we propose a residual-based multi-peaks sampling algorithm. Evaluate the training results of each epoch of neural network, calculate the probability density function P(x) of the residual, perform sampling where the P(x) is large, and add samples to the training set to retrain the neural network. In order to prevent the neural network from falling into the trap of overfitting, we discretize the sampling points. We conduct case studies using two classical nonlinear dynamical systems and perform bifurcation and first escape probability analyzes of the fitted equations. Results show that our proposed sampling strategy requires only 20∼30% of the sample points of the original method to reconstruct the stochastic dynamical behavior of the system. Finally, the algorithm is tested by adding interference noise to the data, and the results show that the sampling strategy has better numerical robustness and stability. Copyright © 2023, The Authors. All rights reserved.

关键词： Dynamical systems

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Rate-dependent tipping-delay phenomenon in a thermoacoustic system with colored noise

arXiv

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arXiv 2020年

作者： Zhang, Xiaoyu Xu, Yong Liu, Qi Kurths, Jürgen Department of Applied Mathematics Northwestern Polytechnical University Xi’an710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xian710072 China Potsdam Institute for Climate Impact Research Potsdam14412 Germany

Tipping is a phenomenon in multistable systems where small changes in inputs cause huge changes in outputs. When the parameter varies within a certain time scale, the rate will affect the tipping behaviors. These behaviors are undesirable in thermoacoustic systems, which are widely used in aviation, power generation and other industries. Thus, this paper aims at considering the tipping behaviors of the thermoacoustic system with the time-varying parameters and the combined excitations of additive and multiplicative colored noises. Transient dynamical behaviors for the proposed thermoacoustic model are implemented through the reduced Fokker-Planck-Kolmogorov equation derived by a standard stochastic averaging method. Then, the tipping problems of the rate-dependent thermoacoustic systems with random fluctuations are studied by virtue of the obtained probability density functions. Our results show that the rate delays the value of the tipping parameter compared to the one with the quasi-steady assumption, which is called as a rate-dependent tipping-delay phenomenon. Besides, the influences of the initial values, the rate, the changing time of the parameters, and the correlation time of the noises on the rate-dependent tipping-delay phenomenon are analyzed in detail. These results are of great significance for research in related fields such as aviation and land gas turbines. Copyright © 2020, The Authors. All rights reserved.

关键词： White noise

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Heterogeneous diffusion processes and nonergodicity with Gaussian colored noise in layered diffusivity landscapes

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Physical Review E 2020年第6期102卷 062106-062106页

作者： Yong Xu Xuemei Liu Yongge Li Ralf Metzler School of Mathematics and Statistics Northwestern Polytechnical University Xi'an 710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'an 710072 China Center for Mathematical Sciences Huazhong University of Science and Technology Wuhan 430074 China Institute for Physics and Astronomy University of Potsdam 14476 Potsdam-Golm Germany

Heterogeneous diffusion processes (HDPs) with space-dependent diffusion coefficients D(x) are found in a number of real-world systems, such as for diffusion of macromolecules or submicron tracers in biological cells. Here, we examine HDPs in quenched-disorder systems with Gaussian colored noise (GCN) characterized by a diffusion coefficient with a power-law dependence on the particle position and with a spatially random scaling exponent. Typically, D(x) is considered to be centerd at the origin and the entire x axis is characterized by a single scaling exponent α. In this work we consider a spatially random scenario: in periodic intervals (“layers”) in space D(x) is centerd to the midpoint of each interval. In each interval the scaling exponent α is randomly chosen from a Gaussian distribution. The effects of the variation of the scaling exponents, the periodicity of the domains (“layer thickness”) of the diffusion coefficient in this stratified system, and the correlation time of the GCN are analyzed numerically in detail. We discuss the regimes of superdiffusion, subdiffusion, and normal diffusion realisable in this system. We observe and quantify the domains where nonergodic and non-Gaussian behaviors emerge in this system. Our results provide new insights into the understanding of weak ergodicity breaking for HDPs driven by colored noise, with potential applications in quenched layered systems, typical model systems for diffusion in biological cells and tissues, as well as for diffusion in geophysical systems.

关键词： Anomalous diffusion Noise Stochastic processes Random & disordered media Ergodic theory

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