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Social tolerance allows cooperation to prevail in an adaptive environment

Physical Review E 2009年第5期80卷 051104-051104页

作者： Xiaojie Chen 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 Department of Zoology University of British Columbia Vancouver British Columbia Canada V6T 1Z4 Program for Evolutionary Dynamics Harvard University Cambridge Massachusetts 02138 USA

In real situations, individuals often have moderate tolerance toward ambient cooperative environment in which they tend to avoid unfavorable interactions and search for favorable ones. How such social tolerance affects the evolution of cooperation and the resulting cooperative networks remains to be answered. To address this issue, here we present an effective model of co-evolutionary prisoner’s dilemma by introducing cooperative environment and social tolerance for networked players. An individual’s level of cooperative environment characterizes the cooperativity and sustainability of its interaction environment centered on itself. In our model, for paired individuals we assume that the one in better cooperative environment has a certain tolerance threshold to the opponent. If the opponent’s cooperative environment level is beyond the tolerance threshold, the one in better cooperative environment cuts unilaterally the link, and rewires to others. Otherwise, the link is not severed, and meanwhile an inhomogeneous strategy imitation process between them is considered. Moreover, a player’s cooperative environment is adjusted in response to the strategy choices in the neighborhood. Interestingly, we find that there exists a moderate tolerance threshold warranting the best promotion of cooperation. We explain the nontrivial results by investigating the time ratio of strategy (network) updating during the whole process and properties in emerging networks. Furthermore, we investigate the effect of memory-dependent discounting of individuals’ cooperative environment on the evolution of cooperation. We also demonstrate the robustness of our results by considering two other modified co-evolutionary rules. Our results highlight the importance of appropriate tolerance threshold for the evolution of cooperation during the entangled co-evolution of strategy and structure.

关键词： Sustainable development

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DIRECT ROBUST ADAPTIVE NONLINEAR control with DERIVATIVES ESTIMATION

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IFAC Proceedings Volumes 2005年第1期38卷 229-234页

作者： D.V. Efimov I.Yu. Tyukin Control of Complex Systems Laboratory Institute of Problem of Mechanical Engineering Bolshoi av. 61 V.O. St-Petersburg 199178 Russia Laboratory for Perceptual Dynamics RIKEN (Institute for Physical and Chemical Research) Brain Science Institute 2-1 Hirosawa Wako-shi Saitama 351-0198 Japan

In this paper we propose a novel adaptive control algorithm which allows to handle the issues of detectability, robustness and transient performance of adaptive systems. The controller structurally is similar to that of Panteley et al (2002). It is designed, however, on the grounds of rather different philosophy – estimation of the derivatives of plant state. In addition to systems which can be rendered to be asymptotically stable by means of the state feedback, plants satisfying assumption of partial asymptotic stability are considered.

关键词： adaptive control robustness persistent excitation

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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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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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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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Averaging principles for non-autonomous two-time-scale stochastic reaction-diffusion equations with polynomial growth

arXiv

引用

arXiv 2019年

作者： Wang, Ruifang Xu, Yong Pei, Bin Department of Applied Mathematics Northwestern Polytechnical University Xi'an710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'an710072 China School of Mathematical Sciences Fudan University Shanghai200433 China

In this paper, we develop the averaging principle for a class of two-time-scale stochastic reaction-diffusion equations driven by Wiener processes and Poisson random measures. We assume that all coefficients of the equation have polynomial growth, and the drift term of the equation is non-Lipschitz. Hence, the classical formulation of the averaging principle under the Lipschitz condition is no longer available. To prove the validity of the averaging principle, the existence and uniqueness of the mild solution are proved firstly. Then, the existence of time-dependent evolution family of measures associated with the fast equation is studied, by which the averaged coefficient is obtained. Finally, the validity of the averaging principle is *** Codes 70K70, 60H15, 34K33, 37B55, 60J75 Copyright © 2019, The Authors. All rights reserved.

关键词： Stochastic 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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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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Convergence of martingale solutions to the hybrid slow-fast system

arXiv

引用

arXiv 2018年

作者： Xu, Yong Yang, Xiaoyu Pei, Bin Bai, Yuzhen School of Mathematics and Statistics Northwestern Polytechnical University Xi’an710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710072 China School of Mathematical Sciences Qufu Normal University Qufu273165 China

This paper is devoted to studying the weak convergence for a slow-fast system with jumps modulated by Markovian switching regimes with the martingale method. However, due to the coexistence of fast component and Markovian switching regimes, the martingale method and perturbed test functions can not be applied directly. In this situation, a combination of perturbed test functions and the time discretization is applied efficiently. And the choice of appropriate perturbed test functions, which are related to the averaged coefficients, plays a decisive role. Our results also cover the case of slow-fast system without Markovian switching regimes. Finally, some examples are presented, and numerical simulations are carried out to observe a good *** Codes 70K70, 60J25, 60G51 Copyright © 2018, The Authors. All rights reserved.

关键词： Markov processes

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Aluminum Nitride Ring Resonator-Coupled Spin Defects in Hexagonal Boron Nitride for Integrated Quantum Photonics

Aluminum Nitride Ring Resonator-Coupled Spin Defects in Hexa...

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CLEO: Science and Innovations in CLEO 2024, CLEO: S and I 2024 - Part of Conference on Lasers and Electro-Optics

作者： Roberts, Henry C. Waseem, Aadil Wicker, Scott A. Abudayyeh, Hamza Kim, Dong Seob Liu, Zhida Randolph, Steven Li, Xiaoqin Li, Xiuling Department of Electrical and Computer Engineering Microelectronics Research Center The University of Texas at Austin 10100 Harry Ransom Trail AustinTX78758 United States Department of Physics Center for Complex Quantum Systems Center for Dynamics Control of Materials Texas Materials Institute The University of Texas at Austin 2515 Speedway AustinTX78712 United States Center for Nanophase Materials Sciences Oak Ridge National Laboratory Oak RidgeTN37830 United States

We report a new approach to generate waveguide-coupled emission from deterministically implanted boron vacancy spin defects in hBN using single-crystal AlN-on-sapphire ring resonators. This facilitates the eventual de... 详细信息

关键词： Single crystals

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