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Parameter effects on high-speed UAV ground directional stability using Bifurcation analysis

Chinese Journal of Aeronautics 2021年第11期34卷 1-14页

作者： Qiaozhi YIN Xiaohui WEI Hong NIE Jian DENG State Key Laboratory of Mechanics and Control of Mechanical Structures Nanjing University of Aeronautics and AstronauticsNanjing 210016China Key Laboratory of Fundamental Science for National Defense-Advanced Design Technology of Flight Vehicle Nanjing University of Aeronautics and AstronauticsNanjing 210016China MIIT Key Laboratory of Multifunctional Lightweight Materials and Structures Nanjing University of Aeronautics and AstronauticsNanjing 210016China

A loss of ground directional stability can trigger a high-speed Unmanned Aerial Vehicle(UAV)to veer off the runway.In order to investigate the combined effects of the key structural and operational parameters on the UAV ground directional stability from a global perspective,a fully parameterized mathematical high-speed UAV ground nonlinear dynamic model is developed considering several nonlinear factors.The Bifurcation analysis procedure of a UAV ground steering system is introduced,following which the simulation efficiency is greatly improved comparing with the time-domain simulation method.Then the numerical continuation method is employed to investigate the influence of the nose wheel steering angle and the global stability region is obtained.The bifurcation parameter plane is divided into several parts with different stability properties by the saddle nodes and the Hopf bifurcation points.We find that the UAV motion states will never cross the bifurcation curve in the nonlinear system.Also,the dual-parameter bifurcation analyses are presented to give a complete description of the possible steering performance.It is also found that BT bifurcation appears when the UAV initial rectilinear velocity and the tire frictional coefficient vary.In addition,results indicate that the influence of tire frictional coefficient has an opposite trend to the influence of initial rectilinear velocity.Overall,using Bifurcation analysis method to identify the parameter regions of a UAV nonlinear ground dynamic system helps to improve the development efficiency and quality during UAV designing phase.

关键词： Bifurcation analysis Ground directional stability High-speed UAV Nonlinear system Numerical continuation

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Bifurcation analysis of visual angle model with anticipated time and stabilizing driving behavior

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Chinese Physics B 2022年第7期31卷 214-228页

作者：管学义程荣军葛红霞 Faculty of Maritime and Transportation Ningbo UniversityNingbo 315211China

In the light of the visual angle model(VAM),an improved car-following model considering driver's visual angle,anticipated time and stabilizing driving behavior is proposed so as to investigate how the driver's behavior factors affect the stability of the traffic flow.Based on the model,linear stability analysis is performed together with Bifurcation analysis,whose corresponding stability condition is highly fit to the results of the linear analysis.Furthermore,the time-dependent Ginzburg–Landau(TDGL)equation and the modified Korteweg–de Vries(m Kd V)equation are derived by nonlinear analysis,and we obtain the relationship of the two equations through the comparison.Finally,parameter calibration and numerical simulation are conducted to verify the validity of the theoretical analysis,whose results are highly consistent with the theoretical analysis.

关键词： visual angle Bifurcation analysis anticipated time stabilizing driving behavior TDGL and mKdV equations

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Exact solutions of a time-fractional modified KdV equation via Bifurcation analysis

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Chinese Physics B 2023年第12期32卷 192-199页

作者：刘敏远许慧王增桂 School of Mathematical Sciences Liaocheng UniversityLiaocheng 252059China

The time-fractional modified Korteweg-de Vries(KdV)equation is committed to establish exact solutions by employing the bifurcation method.Firstly,the phase portraits and related qualitative analysis are comprehensively provided.Then,we give parametric expressions of different types of solutions matching with the corresponding orbits.Finally,solution profiles,3D and density plots of some solutions are presented with proper parametric choices.

关键词： the time-fractional modified KdV equation Bifurcation analysis exact solutions

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Bifurcation analysis for a Free Boundary Problem Modeling Growth of Solid Tumor with Inhibitors

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Communications in Mathematical Research 2017年第1期33卷 85-96页

作者： Wang Ze-jia Xu Jian-lei Li Jing-hua College of Mathematics and Information Science Jiangxi Normal UniversityNanchang 330022

This paper is concerned with the Bifurcation analysis for a free boundary problem modeling the growth of solid tumor with inhibitors.In this problem,surface tension coefficient plays the role of bifurcation parameter,it is proved that there exists a sequence of the nonradially stationary solutions bifurcate from the radially symmetric stationary solutions.Our results indicate that the tumor grown in vivo may have various shapes.In particular,a tumor with an inhibitor is associated with the growth of protrusions.

关键词： free boundary problem Bifurcation analysis solid tumor

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Bifurcation analysis of mixed bursting in the pre-B?tzinger complex

Bifurcation analysis of mixed bursting in the pre-B?tzinger ...

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第四届全国神经动力学学术会议

作者：吕卓生陈立纳郭豆豆张珂 School of Science Beijing University of Posts and Telecommunications

Activity of neurons in the pre-B?tzinger complex(pre-B?tC) within the mammalian brainstem has an important role in the generation and regulation of respiratory rhythms. Previous experimental results have shown that both the persistent sodium current and an intracellular Ca2+ active nonspecific cation can drive the mixed bursting in the pre-B?tC. In this work, we consider a single-compartment model of a pre-B?tC inspiratory neuron that has the ability to produce mixed bursting solutions. Using a combination of fast-slow decomposition and Bifurcation analysis, we study the dynamical mechanisms underlying the mixed bursting solution pattern, and investigate the effects of sodium conductance and potassium conductance on the mixed bursting patterns of the pre-B?tC.Furthermore, we elucidate the effects of parameters potassium conductance and leak conductance on the number of somatic bursts in a mixed bursting solution. This work may provide insights of how ionic currents work on the respiratory rhythm generation.

关键词： Pre-B?tzinger complex Mixed bursting Bifurcation analysis Fast-slow decomposition

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Bifurcation analysis of a Nonlinear Genetic Network Model with Time Delay

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Journal of Applied Mathematics and Physics 2023年第8期11卷 2252-2266页

作者： Anael Verdugo Department of Mathematics California State University Fullerton USA

This paper presents a bifurcation study of a mRNA-protein network with negative feedback and time delay. The network is modeled as a coupled system of N ordinary differential equations (ODEs) and N delay differential equations (DDEs). Linear analysis of the stable equilibria shows the existence of a critical time delay beyond which limit cycle oscillations are born in a Hopf bifurcation. The Poincaré-Lindstedt perturbation method is applied to the nonlinear system, resulting in closed form approximate expressions for the amplitude and frequency of oscillation. We confirm our perturbation analysis results by numerically simulating the full 2N-dimensional nonlinear system for N = 2, 7, 15, and 30. Our results show that for small perturbations the equilibrium undergoes a supercritical Hopf and the system exhibits stable periodic solutions. Furthermore, our closed form numerical expressions exhibit the importance of the network’s negative feedback and nonlinear effects.

关键词： Bifurcation analysis Hopf Delay Differential Equations

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Bifurcation analysis OF NEARLY NONSMOOTH OSCILLATIONS IN INPUT-CONSTRAINED FLIGHT CONTROL SYSTEMS

BIFURCATION ANALYSIS OF NEARLY NONSMOOTH OSCILLATIONS IN INP...

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The Third International Conference on Dynamics, Vibration and Control

作者： M.Demenkov Nonlinear Dynamics ＆ Control Lab Institute of Control SciencesMoscowRussia

＜正＞Numerical Bifurcation analysis using continuation methods has emerged as a valuable component in the analysis of mathematical models described by differential equations.The application of Bifurcation analysis to flight control problems began in the early 1980s.So far,numerical continuation has been employed many times for the analysis of particular flight regimes,although its industrial applications remain quite limited.In several publications Bifurcation analysis has been posed as a method for clearance（i.***.verification） of modern flight control laws as well as a supplementary tool for their design.

关键词： Flight control nonlinear system control constraints Bifurcation analysis limit cycle

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Nonlinear dynamic response and stability analysis of the stapes reconstruction in human middle ear

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应用数学和力学:英文版 2023年第10期44卷 1739-1760页

作者： Lele WANG Liang WANG Yueting ZHU Zhanli LIU Yongtao SUN Jie WANG Hongge HAN Shuyi XIANG Huibin SHI Qian DING Department of Mechanics Tianjin UniversityTianjin 300350China Tianjin Key Laboratory of Nonlinear Dynamics and Control Tianjin UniversityTianjin 300350China Department of Otolaryngology Head and Neck SurgeryTianjin Children's HospitalTianjin UniversityTianjin 300400China School of Aerospace Engineering Tsinghua UniversityBeijing 100084China Department of Otolaryngology Head and Neck Surgery Beijing Tongren HospitalCapital Medical UniversityBeijing 100730China Key Laboratory of Otolaryngology Head and Neck Surgery Ministry of EducationBeijing 100730China Beijing Engineering Research Center of Audiological Technology Beijing 100730China

Stapes fracture causes hearing loss and instability in the middle ear hearing system(MEHS). The material used in the stapes reconstruction restores stapes, but the effects of the nonlinear material parameters on the stability of the MEHS are still unknown. To address this challenge, the nonlinear dynamic response and stability of the stapes reconstruction are investigated using a multi-degree-of-freedom mechanical model. The material parameters of the implant are tentatively determined by analyzing the natural frequencies of the undamped system. The dynamical properties of the MEHS are characterized under different external excitations. The approximate solution of the MEHS near the resonant frequency is derived through the multiple-time-scale method(MTSM). The results show that the nonlinear stiffness of the material has little influence on the MEHS in the healthy state, but it causes resonant phenomena between the ossicle and the implant in the pathological state.

关键词： crus fracture of stapes stapes reconstruction dynamic analysis Bifurcation analysis multiple-time-scale method(MTSM)

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Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor

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Chinese Physics B 2022年第10期31卷 331-340页

作者：张丽萍刘洋魏周超姜海波吕伟鹏毕勤胜 Faculty of Civil Engineering and Mechanics Jiangsu UniversityZhenjiang 212013China School of Mathematics and Statistics Yancheng Teachers UniversityYancheng 224002China Engineering Department Mathematics and Physical SciencesUniversity of ExeterExeter EX44QFUK School of Mathematics and Physics China University of GeosciencesWuhan 430074China

We present a class of two-dimensional memristive maps with a cosine memristor. The memristive maps do not have any fixed points, so they belong to the category of nonlinear maps with hidden attractors. The rich dynamical behaviors of these maps are studied and investigated using different numerical tools, including phase portrait, basins of attraction,bifurcation diagram, and Lyapunov exponents. The two-parameter Bifurcation analysis of the memristive map is carried out to reveal the bifurcation mechanism of its dynamical behaviors. Based on our extensive simulation studies, the proposed memristive maps can produce hidden periodic, chaotic, and hyper-chaotic attractors, exhibiting extremely hidden multistability, namely the coexistence of infinite hidden attractors, which was rarely observed in memristive maps. Potentially,this work can be used for some real applications in secure communication, such as data and image encryptions.

关键词： two-dimensional maps memristive maps hidden attractors Bifurcation analysis extremely hidden multi-stability

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Complex Dynamical Behaviors in a Dual Channel Supply Chain Model with Retailer's Service Input

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Journal of Systems Science & Complexity 2023年第3期36卷 1144-1168页

作者： ZHANG Yapeng ZHOU Wei School of Mathematics and Physics Lanzhou Jiaotong UniversityLanzhou 730070China School of Traffic and Transportation Lanzhou Jiaotong UniversityLanzhou 730070China Key Laboratory of Railway Industry of Plateau Railway Transportation Intelligent Management and Control Lanzhou 730070China

Based on bounded rationality,this paper established a price game model of dual channel supply chain composed of manufacturers and retailers.According to the eigenvalue of Jacobi matrix and Jury criterion,the stability of the equilibrium point is analyzed,and then the dynamic evolution process under the parameters of price adjustment speed and retailer's service input is studied through stability region,bifurcation diagram,maximum Lyapunov exponent diagram and attraction basin.The results show that the system enters chaos through flip and Neimark-Sacker bifurcation,and increase of price adjustment speed and service input value will make the system produce more dynamic behavior.In addition,it can be found that the impact of service input value on itself is much greater than that on manufacturers.Secondly,when adjustment speed is selected as bifurcation parameter,the change curve of sales price is inconsistent,in which the change of retailers mainly remains in periodic state,while manufacturers will gradually enter chaos.Finally,studies the evolution of attraction basin in which three kinds of attractors coexist.In particular,coexistence of boundary attractors and internal attractors increases the complexity of system.Therefore,enterprises need to carefully adjust parameters of the game model to control the stability of system and maintain the long-term stability of market competition.

关键词： Bifurcation analysis boundary equilibrium coexistence of attractors flip bifurcation global bifurcation

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