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Astrodynamics 2018年第4期2卷 361-373页

作者： Yu Jiang State Key Laboratory of Astronautic Dynamics Xi’an Satellite Control CenterXi’an710043China School of Aerospace Engineering Tsinghua UniversityBeijing100084China

We investigate the equilibrium points and orbits around asteroid 1333 Cevenola by considering the full gravitational potential caused by the 3D irregular *** gravitational potential and effective potential of asteroid 1333 Cevenola are *** zero-velocity curves for a massless particle orbiting in the gravitational environment have been *** linearized dynamic equation,the characteristic equation,and the conserved quantity of the equilibria for the large-size-ratio binary asteroid system have been *** is found that there are totally five equilibrium points close to 1333 *** topological cases of the outside equilibrium points have a staggered *** simulation of orbits in the full gravitational potential caused by the 3D irregular shape of 1333 Cevenola shows that the moonlet’s orbit is more likely to be stable if the orbit inclination is small.

关键词： equilibrium points orbits polyhedral model asteroids 1333 Cevenola

Constant Thrust Control Based on Double Threshold for Hovering at Asteroid equilibrium points 32

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Constant Thrust Control Based on Double Threshold for Hoveri...

Fractional-order systems without equilibria:The first example of hyperchaos and its application to synchronization

第32届中国控制与决策会议

作者： SUI Zhihui FENG Junhua LI Maodeng ZHU Shengying School of Aerospace Engineering Beijing Institute of Technology Key Laboratory of Autonomous Navigation and Control for Deep Space Exploration National Key Laboratory of astrodynamics Key Laboratory of Science and Technology on Space Intelligent Control Beijing Institute of Control Engineering

ISBN: (数字)9781728158556

ISBN: (纸本)9781728158563

This paper proposes a dual-threshold control method for constant thrust of hovering orbit at the unstable equilibrium point of an ***,according to the orbital dynamics model of the probe,the nominal hover ing orbit of the probe near the equilibrium point is ***,according to the basic idea of threshold control,not only set the threshold at the current moment,but also predict the state of the future moment and set the threshold at that *** when both thresholds are triggered at the same time does the constant thrust engine come into operation,which keeps the detector on the hovering ***,simulation was performed with Eros433 as the target *** simulation results show that the method can effectively reduce the number of engines switching and operating time while maintaining a certain accuracy.

关键词： equilibrium points Constant thrust Dual-threshold control Nominal hover orbit

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Chinese Physics B 2015年第8期24卷 224-232页

作者： Donato Cafagna Giuseppe Grassi Dipartimento Ingegneria Innovazione Università del Salento

A challenging topic in nonlinear dynamics concerns the study of fractional-order systems without equilibrium *** particular, no paper has been published to date regarding the presence of hyperchaos in these systems. This paper aims to bridge the gap by introducing a new example of fractional-order hyperchaotic system without equilibrium points. The conducted analysis shows that hyperchaos exists in the proposed system when its order is as low as 3.84. Moreover, an interesting application of hyperchaotic synchronization to the considered fractional-order system is provided.

关键词： fractional-order systems equilibrium points hyperchaotic systems synchronization

Study on periodic orbits around the dipole segment model for dumbbell-shaped asteroids

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Science China(Technological Sciences) 2018年第6期61卷 819-829页

作者： ZHANG YongLong ZENG XiangYuan LIU XiangDong School of Automation Beijing Institute of Technology Beijing 100081 China

equilibrium points and periodic orbits in irregular gravitational fields are significant for an understanding of dynamical behaviors around asteroids as well as deep space exploring missions. The dipole segment is a good alternative model to study qualitative dynamical properties near dumbbell-shaped asteroids. In this paper, the dipole segment model and its equilibrium points are simply introduced. The stability of the two triangular equilibrium points of the system is numerically examined. Next, periodic orbits are presented around the dipole segment model in two different cases, in which triangular equilibria are linearly stable and unstable,respectively. New types of periodic orbits are illustrated in detail, including their orbital shapes, periods and the Jacobi *** orbital stability, topological classification and bifurcations of these orbits are also analyzed with numerical continuations.

关键词： dipole segment model equilibrium points periodic orbits topological classification

Co-existence thresholds in the dynamics of the plant-herbivore interaction with Allee effect and harvest

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International Journal of Biomathematics 2018年第4期11卷 229-255页

作者： Manalebish Debalike Asfaw Semu Mitiku Kassa Edward M. Lungu2 Department of Mathematics Addis Ababa University P.O. Box 1176 Addis Ababa Ethiopia Department of Mathematics and Statistical Sciences Botswana International University of Science andTechnology (BIUST) P/Bag 16 Palapye Botswana

In the interaction between plants and herbivores that live in the same ecosystem, understanding the conditions in which co-existence equilibrium occurs answers a major question in Ecology. In this interaction, plants serve as food for herbivores on the food chain. Then the livelihood of herbivores highly depends on the availability of food, in this case the availability of plants. Moreover, the abundance of the plant density alone does not guarantee the non-extinction of the herbivore population as they are assumed to reproduce sexually. With this motivation, in this paper a predator-prey mathematical model is reformulated such that the death rate of the herbivore population is dependent on the plant density and their emergence is also governed by the Allee effect. Using the mathematical theory of dynamical system, threshold conditions are obtained for the non-extinction of the herbivore population and a trapping region is obtained to ensure co-existence of the population. Moreover, it has been shown that the dynamics of the population is significantly sensitive to the feeding rate and the harvest rate of the herbivore population.

关键词： Predator-prey Allee effect harvest equilibrium points threshold sensitivityanalysis.

A Nonlinear Coupled Soil Moisture-Vegetation Model

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Advances in Atmospheric Sciences 2005年第3期22卷 337-342页

作者：刘式适刘式达付遵涛孙岚 School of Physics & Laboratory for Severe Storm and Flood DisasterPeking University Beijing 100871 School of Physics & Laboratory for Severe Storm and Flood DisasterPeking University Beijing 100871 State Key Laboratory for Turbulence and Complex Systems Peking University Beijing 100871 School of Physics & Laboratory for Severe Storm and Flood Disaster Peking University Beijing 100871 State Key Laboratory for Turbulence and Complex Systems Peking University Beijing 100871 Chinese Academy of Meteorological Sciences Beijing 100081

Based on the physical analysis that the soil moisture and vegetation depend mainly on the precipitation and evaporation as well as the growth, decay and consumption of vegetation a nonlinear dynamic coupled system of soil moisture-vegetation is established. Using this model, the stabilities of the steady states of vegetation are analyzed. This paper focuses on the research of the vegetation catastrophe point which represents the transition between aridness and wetness to a great extent. It is shown that the catastrophe point of steady states of vegetation depends mainly on the rainfall P and saturation value υ0, which is selected to balance the growth and decay of vegetation. In addition, when the consumption of vegetation remains constant, the analytic solution of the vegetation equation is obtained.

关键词： vegetation steady states equilibrium points catastrophe point cusp catastrophe

HOPF BIFURCATION FOR A ECOLOGICAL MATHEMATICAL MODEL ON MICROBE POPULATIONS

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Applied Mathematics and Mechanics(English Edition) 2000年第7期21卷 767-774页

作者：郭瑞海袁晓凤 Department of Mathematics Southwest Nationalities College Chengdu P R China Center for Mathematical Sciences CICA Academia Sinica Chengdu P R China

The ecological model of a class of the two microbe populations with second-order growth rate was studied. The methods of qualitative theory of ordinary differential equations were used in the four-dimension phase space. The qualitative property and stability of equilibrium points were analysed. The conditions under which the positive equilibrium point exists and becomes and O+ attractor are obtained. The problems on Hopf bifurcation are discussed in detail when small perturbation occurs.

关键词： mathematical model qualitative theory equilibrium points Hopf bifurcation

Analysis of a hand-foot-mouth disease model

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International Journal of Biomathematics 2017年第2期10卷 1-47页

作者： Swarnali Sharma G. P. Samanta Department of MathematicsIndian Institute of Engineering Science and Technology Shibpur Howrah 711103 India

In this paper, we have introduced a six-compartmental epidemic model with hand, foot and mouth disease （HFMD） infection. The total population is divided into six subclasses, namely susceptible, exposed, infective in asymptomatic phase, infective in symptomatic phase, quarantined and recovered class. Some basic properties such as boundedness and non-negativity of solutions are discussed. The basic reproduction number （R0） of the system is obtained using next generation matrix method. Then the deterministic dynamical behaviors of the system are studied. Our study includes the existence and stability analysis of equilibrium points of the system. The sensitivity analysis of our system helps us to find out the parameters of greater interest. Next, we deal with the epidemic model with three controls （two treatment controls with quarantine control）. We show that there exists an optimal control, which is effective in controlling the disease outbreak in a cost effective way. Numerical simulation is presented with the help of MATLAB, which shows tile reliability of our model from the practical point of view.

关键词： Hand, foot and mouth disease (HFMD) infection basic reproduction number equilibrium points local and global stability optimal control.

IMPULSIVE CONTROL IN MICROORGANISMS CONTINUOUS FERMENTATION

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International Journal of Biomathematics 2012年第2期5卷 33-41页

作者： LIJUAN SHEN ENMIN FENG QIDI WU Department of Control Science and EngineeringTongji University Shanghai 200092 P. R. China Department of Mathematics Luoyang Normal University Luoyang 371022 P. R. China Department of Applied Mathematics Dalian University of Technology Dalian 116024 P. R. China Department of Control Science and Engineering Tongji University Shanghai 200092 P. R. China

This work presents the nonlinear dynamical system of continuous fermentation from glycerol to 1,3-propanediol. The impulsive control scheme of continuous culture is intro- duced. By employing impulsive control, Lyapunov＇s method and comparison technique, sufficient conditions are established for the asymptotical stability and synchronization of the dynamical system of continuous fermentation. The upper bound of the impulse interval is also estimated. An example will illustrate the effectiveness of the results in Sec. 4.

关键词： Nonlinear dynamical system equilibrium points asymptotical stability impulsive control.

Modeling and stability analysis of the spread of novel coronavirus disease COVTD-19

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International Journal of Biomathematics 2021年第5期14卷 239-272页

作者： A.George Maria Selvam Jehad Alzabut D.Abraham Vianny Mary Jacintha Fatma Bozkurt Yousef PG and Research Department of Mathematics Sacred Heart College(Autonomous) Tirupattur 635601India Department of Mathematics and Science Education Faculty of Education Erciyes University38039 KayseriTurkey Department of Mathematics and General Sciences Prince Sultan University 11586 RiyadhSaudi Arabia Department of Mathematics Kuwait College of Science and Technology 27235 Kuwait City Kuwait

Towards the end of 2019,the world witnessed the outbreak of Severe Acute Respiratory Syndrome Coronavirus-2(COVID-19),a new strain of coronavirus that was unidentified in humans *** this paper,a new fractional-order Susceptible-Exposed-Infected-Hospitalized-Recovered(SEIHR)model is formulated for COVID-19,where the population is infected due to human *** fractional-order discrete version of the model is obtained by the process of discretization and the basic reproductive number is calculated with the next-generation matrix *** equilibrium points related to the disease transmission model are then ***,sufficient conditions to investigate all possible equilibria of the model are established in terms of the basic reproduction number(local stability)and are supported with time series,phase portraits and bifurcation ***,numerical simulations are provided to demonstrate the theoretical findings.

关键词： Discrete fractional order SEIHR model equilibrium points stability bifurcation