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Dynamical analysis for the sustained harvesting of microorganisms using flocculants in a random environment

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Chinese Physics B 2023年第5期32卷 343-349页

作者：刘蓉马万彪 School of Mathematics and Physics University of Science and Technology BeijingBeijing 100083China School of Science Chongqing University of Posts and TelecommunicationsChongqing 400065China

The use of flocculants to collect/extract microorganisms is of great practical significance for the development of the application of microorganisms. In this paper, a high-dimensional nonlinear stochastic differential equation model is constructed to describe the continuous culture of microorganisms with multiple nutrients and the flocculation process of microorganisms. The study of the dynamics of this model can provide feasible control strategies for the collection/extraction of microorganisms. The main theoretical results are sufficient conditions for the permanence and extinction of the stochastic differential equation model, which are also extensions of some results in the existing literatures. In addition, through numerical simulations, we vividly demonstrate the statistical characteristics of the stochastic differential equation model.

关键词： stochastic process stochastically ultimately bounded stochastic permanence noise-induced transitions

Near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters

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Chinese Physics B 2021年第12期30卷 182-194页

作者： Liang’an Huo Xiaomin Chen Business School University of Shanghai for Science and TechnologyShanghai 200093China

In recent years,rumor spreading has caused widespread public panic and affected the whole social harmony and ***,how to control the rumor spreading effectively and reduce its negative influence urgently needs people to pay much *** this paper,we mainly study the near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise ***,the science knowledge propagation and the refutation mechanism as the control strategies are introduced into a stochastic rumor spreading ***,some sufficient and necessary conditions for the near-optimal control of the stochastic rumor spreading model are discussed ***,through some numerical simulations,the validity and availability of theoretical analysis is ***,it shows the significance and effectiveness of the proposed control strategies on controlling rumor spreading,and demonstrates the influence of stochastic disturbance and imprecise parameters on the process of rumor spreading.

关键词： rumor spreading HollingⅡfunctional response function near-optimal control stochastic process

Lyapunov function as potential function: A dynamical equivalence

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Chinese Physics B 2014年第1期23卷 136-141页

作者：袁若石马易安苑波敖平 School of Biomedical Engineering Shanghai Jiao Tong University Shanghai Center for Systems Biomedicine Shanghai Jiao Tong University Department of Applied Mathematics University of Washington Department of Computer Science and Engineering Shanghai Jiao Tong University Department of Physics Shanghai Jiao Tong University

For a physical system, regardless of time reversal symmetry, a potential function serves also as a Lyapunov function, providing convergence and stability information. In this paper, the converse is constructively proved that any dynamics with a Lyapunov function has a corresponding physical realization： a friction force, a Lorentz force, and a potential function. Such construction establishes a set of equations with physical meaning for Lyapunov function and suggests new approaches on the significant unsolved problem namely to construct Lyapunov functions for general nonlinear systems. In addition, a connection is found that the Lyapunov equation is a reduced form of a generalized Einstein relation for linear systems, revealing further insights of the construction.

关键词： Lyapunov function potential function stochastic process generalized Einstein relation

Synthetic Time Series Generation Model for Analysis of Power System Operation and Expansion with High Renewable Energy Penetration

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Journal of Modern Power Systems and Clean Energy 2021年第4期9卷 849-858页

作者： Rodrigo Palma-Behnke Jorge Vega-Herrera Felipe Valencia Oscar Nunez-Mata Energy Center Department of Electrical EngineeringFaculty of Mathematical and Physical SciencesUniversity of ChileSantiagoChile Department of Electrical Engineering University of AntofagastaAntofagastaChile School of Electrical Engineering University of Costa RicaSan PedroCosta Rica

The increasing integration of renewable energy sources into current power systems has posed the challenge of adequately representing the statistical properties associated with their variable power generation. In this paper, a novel procedure is proposed to select a proper synthetic time series generation model for renewable energy sources to analyze power system problems. The procedure takes advantage of the objective of the specific analysis to be performed and the statistical characteristics of the available time series. The aim is to determine the suitable model to be used for generating synthetic time series of renewable energy sources. A set of indicators is proposed to verify that the statistical properties of synthetic time series fit the statistical properties of the original data. The proposal can be integrated into systematic tools available for data analysis without compromising the representation of the statistical properties of the original time series. The procedure is tested using real data from the New Zealand power system in a mid-term analysis on integrating wind power plants into the power system. The results show that the proposed procedure reduces the error obtained in analyzing power systems compared with reference models.

关键词： Time series analysis renewable energy source solar energy stochastic process statistical analysis wind energy

Dynamics of a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise

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Chinese Physics B 2021年第8期30卷 182-190页

作者： Liang-An Huo Ya-Fang Dong Ting-Ting Lin Business School University of Shanghai for Science and TechnologyShanghai 200093China School of Electrical and Information Engineering Shanghai Jiao Tong UniversityShanghai 200240China

With the development of information technology,rumors propagate faster and more widely than in the *** this paper,a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise is *** global positivity of the solution process is proved,and further the basic reproductive number R_(0) is *** R_(0)process of system with Lévy jump tends to the rumor-free equilibrium point of the deterministic system,and the rumor tends to extinction;when R_(0)>1,the rumor will keep spreading and the system will oscillate randomly near the rumor equilibrium point of the deterministic *** results show that the oscillation amplitude is related to the disturbance of the *** addition,increasing media coverage can effectively reduce the final spread of ***,the above results are verified by numerical simulation.

关键词： rumor propagation stochastic process Lévy jump media coverage

Comparison of two reliability models for performance degradation analysis

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航空动力学报 2015年第7期30卷 1632-1637页

作者： WANG Zhi-hua ZANG Guang-kui ZHANG Yong-bo FU Hui-min Research Center of Small Sample Technology Beijing University of Aeronautics and Astronautics

In order to investigate the general reliability assessment methods based on performance degradation data,two commonly used stochastic process approaches,bilinear process method and random-effect model were *** procedure and effectiveness of these two methodologies were studied and ***,the two approaches were illustrated through practical *** residual plots and the 10th percentile curves of the two methods were presented to demonstrate the comparative *** randomeffect model yielded more volatile residuals and a lower and unsafe 10th percentile *** the bilinear process model can be concluded to derive more reasonable results due to its one-stage estimation property.

关键词： degradation analysis reliability assessment stochastic process bilinear independent increment process random-effect model

stochastic stability of the derivative unscented Kalman filter

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Chinese Physics B 2015年第7期24卷 64-73页

作者：胡高歌高社生种永民高兵兵 School of Automatics Northwestern Polytechnical University School of Aerospace Mechanical and Manufacturing EngineeringRMIT University

This is the second of two consecutive papers focusing on the filtering algorithm for a nonlinear stochastic discretetime system with linear system state equation. The first paper established a derivative unscented Kalman filter（DUKF） to eliminate the redundant computational load of the unscented Kalman filter（UKF） due to the use of unscented transformation（UT） in the prediction process. The present paper studies the error behavior of the DUKF using the boundedness property of stochastic processes. It is proved that the estimation error of the DUKF remains bounded if the system satisfies certain conditions. Furthermore, it is shown that the design of the measurement noise covariance matrix plays an important role in improvement of the algorithm stability. The DUKF can be significantly stabilized by adding small quantities to the measurement noise covariance matrix in the presence of large initial error. Simulation results demonstrate the effectiveness of the proposed technique.

关键词： nonlinear stochastic system stochastic process unscented Kalman filter stochastic stability

Non-Gaussian normal diffusion in low dimensional systems

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Frontiers of physics 2021年第3期16卷 85-98页

作者： Qingqing Yin Yunyun Li Fabio Marchesoni Subhadip Nayak Pulak K.Ghosh Center for Phononics and Thermal Energy Science Shanghai Key Laboratory of Special Artificial Microstructure Materials and TechnologySchool of Physics Science and EngineeringTongji UniversityShanghai200092China Dipartimento di Fisica Universitàdi CamerinoI-62032CamerinoItaly Department of Chemistry Presidency UniversityKolkata700073India

Brownian particles suspended in disordered crowded environments often exhibit non-Gaussian normal diffusion(NGND),whereby their displacements grow with mean square proportional to the observation time and non-Gaussian *** distributions appear to decay almost exponentially according to“universal”laws largely insensitive to the observation *** effect is generically attributed to slow environmental fluctuations,which perturb the local configuration of the suspension *** investigate the microscopic mechanisms responsible for the NGND phenomenon,we study Brownian diffusion in low dimensional systems,like the free diffusion of ellipsoidal and active particles,the diffusion of colloidal particles in fluctuating corrugated channels and Brownian motion in arrays of planar convective *** appears to be a transient effect related to the time modulation of the instantaneous particle’s diffusivity,which can occur even under equilibrium ***,we propose to generalize the definition of NGND to include transient displacement distributions which vary continuously with the observation *** this purpose,we provide a heuristic one-parameter function,which fits all time-dependent transient displacement distributions corresponding to the same diffusion ***,we reveal the existence of low dimensional systems where the NGND distributions are not leptokurtic(fat exponential tails),as often reported in the literature,but platykurtic(thin sub-Gaussian tails),i.e.,with negative excess *** actual nature of the NGND transients is related to the specific microscopic dynamics of the diffusing particle.

关键词： non-Gaussian normal diffusion transport phenomena stochastic process active matter

THE AVERAGE ABUNDANCE FUNCTION WITH MUTATION OF THE MULTI-PLAYER SNOWDRIFT EVOLUTIONARY GAME MODEL

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Acta Mathematica Scientia 2021年第1期41卷 127-163页

作者： Ke XIA Xianjia WAiVG School of Economics Zhengzhou University of AeronauticsZhengzhou 450000China School of Economics and Management Wuhan UniversityWuhan 430072China

This article explores the characteristics of the average abundance function with mutation on the basis of the multi-player snowdrift evolutionary game model by analytical analysis and numerical *** specific field of this research concerns the approximate expressions of the average abundance function with mutation on the basis of different levels of selection intensity and an analysis of the results of numerical simulation on the basis of the intuitive expression of the average abundance *** addition,the biological background of this research lies in research on the effects of mutation,which is regarded as a biological concept and a disturbance to game behavior on the average abundance *** mutation will make the evolutionary result get closer to the neutral drift *** can be deduced that this affection is not only related to mutation,but also related to selection intensity and the gap between payoff and aspiration *** main research findings contain four ***,we have deduced the concrete expression of the expected payoff *** asymptotic property and change trend of the expected payoff function has been basically *** addition,the intuitive expression of the average abundance function with mutation has been obtained by taking the detailed balance condition as the point of *** can be deduced that the effect of mutation is to make the average abundance function get close to 1/*** addition,this affection is related to selection intensity and the ***,the first-order Taylor expansion of the average abundance function has been deduced for when selection intensity is sufficiently *** expression of the average abundance function with mutation can be simplified from a composite function to a linear function because of this Taylor *** finding will play a significant role when analyzing the results of the numerical ***,we have obtained the approximate expressions of

关键词： evolutionary game average abundance function mutation stochastic process