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研究了一类具有时滞及非线性发生率的SIR传染病模型.首先利用特征值理论分析了地方病平衡点的稳定性,并以时滞为分岔参数,给出了Hopf分岔存在的条件.然后,应用规范型和中心流形定理给出了关于Hopf分岔周期解的稳定性及分岔方向的计算公式.最后,用Matlab软件进行了数值模拟. 相似文献
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针对三轴重型汽车建立了二自由度非线性人-车-路闭环模型,考虑驾驶员控制和路面方向扰动,推导了系统动力学方程.在运用Hopf分岔理论进行分析的基础上,以临界车速为评价指标,通过数值模拟研究了轴距、预瞄距离、载重量、驾驶员控制时滞和轮胎侧偏刚度对转向稳定性的影响,并确定了转向系统的数值稳定范围.另外,还通过分岔图、时程曲线、相轨线、功率谱、Poincaré图和Lyapunov指数研究了不同车速下汽车的非线性动力学响应.结果表明,随着车速的增加汽车可能发生周期运动、拟周期运动及混沌运动,汽车的横向稳定性与车辆和驾驶员参数密切相关. 相似文献
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运用非线性动力学理论,对一类四维混沌Lorenz系统在平衡点的稳定性问题和Hopf分岔的存在性进行了研究.利用第一Lyapunov系数法给出系统Hopf分岔周期解的稳定性条件.最后,通过数值仿真验证了理论推导的正确性. 相似文献
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流体诱发水平悬臂输液管的内共振和模态转换(Ⅱ) 总被引:1,自引:1,他引:0
基于得到的水平悬臂输液管非线性动力学控制方程,详细研究了由流速最小临界值诱发的3∶1内共振.通过观察内共振调谐参数、主共振调谐参数和外激励幅值的变化,发现在内共振临界流速附近,流速导致系统出现模态转换、鞍结分岔、Hopf分岔、余维2分岔和倍周期分岔等非线性动力学行为,对应的管道系统的周期运动失稳出现跳跃、颤振和更加复杂的动力学行为.通过理论结果与数值模拟比较,表明了理论分析的有效性和正确性. 相似文献
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圆形三向网架非线性动力稳定性分析 总被引:7,自引:2,他引:5
用拟板法将网架简化为平板,给出表层应变与中面位移的非线性关系.根据薄板的非线性动力学理论,建立了在直角坐标系中三向网架的非线性动力学方程,又将此方程转化为极坐标系轴对称非线性动力学方程.在周边固定条件下,引入异于等厚度板的无量纲量,对基本方程无量纲化.利用Galerkin法得到一个三次非线性振动方程,在无外激励情况下,讨论了稳定性与分岔问题.在外激励情况下,用Melnikov方法研究了圆形三向网架可能发生的混沌运动.通过数字仿真绘出了发生混沌的相平面图. 相似文献
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考虑径向内间隙的滚动轴承平衡转子系统的非线性动力稳定性 总被引:9,自引:0,他引:9
研究滚动轴承平衡转子系统在不同轴承内间隙量,不同转速下系统的稳定性及其分岔特性和混沌.考虑Hertz接触力、 滚动体通过振动和轴承径向内间隙等非线性因素建立数学模型,根据Floquet理论分析不同间隙量下滚动轴承转子系统的周期解稳定性, 找到了3种导致周期解失稳的方式:倍周期分岔失稳、拟周期分岔失稳和边界激变导致混沌失稳.通过对各间隙量下转子系统拓扑特性变化和失稳区域的研究,表明滚动轴承间隙量是影响转子系统动力稳定性的一个重要因素. 相似文献
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We consider a plankton-nutrient interaction model consisting of phytoplankton, zooplankton and dissolved limiting nutrient with general nutrient uptake functions and instantaneous nutrient recycling. In this model, it is assumed that phytoplankton releases toxic chemical for self defense against their predators. The model system is studied analytically and the threshold values for the existence and stability of various steady states are worked out. It is observed that if the maximal zooplankton conversion rate crosses a certain critical value, the system enters into Hopf bifurcation. Finally it is observed that to control the planktonic bloom and to maintain stability around the coexistence equilibrium we have to control the nutrient input rate specially caused by artificial eutrophication. In case if it is not possible to control the nutrient input rate, one could use toxic phytoplankton to prevent the recurrence bloom. 相似文献
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Xuanliang Liu 《Applied mathematics and computation》2011,218(5):2300-2309
A predator-prey system with disease in the prey is considered. Assume that the incidence rate is nonlinear, we analyse the boundedness of solutions and local stability of equilibria, by using bifurcation methods and techniques, we study Bogdanov-Takens bifurcation near a boundary equilibrium, and obtain a saddle-node bifurcation curve, a Hopf bifurcation curve and a homoclinic bifurcation curve. The Hopf bifurcation and generalized Hopf bifurcation near the positive equilibrium is analyzed, one or two limit cycles is also discussed. 相似文献
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一类高次自催化耦合反应扩散系统的分歧和斑图 总被引:1,自引:0,他引:1
考虑了一类由于自催化剂的耦合而发生的反应扩散系统的空间结构.利用线性化理论讨论了平衡态解的稳定性并且证明了在非耦合系统中空间非一致解出现分歧的必要条件.进一步,利用弱非线性理论讨论了分歧点并且给出了弱耦合系统的图灵分歧解的振幅方程及其性质. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2011,16(2):769-775
The dynamical behavior of a micro-electromechanical nonlinear coupling system – deformable micromirror device, is investigated in this paper. In the literature some nonlinear phenomena have been explored by using the numerical method, and saddle-node bifurcation and periodic motions were discovered numerically. Overcoming the obstacle of the unsolvable of the equilibrium points, we analytically obtain the number and stability of the equilibrium points of the system discussed. The saddle-node bifurcation is obtained through the analytic method. Further, both codimension two bifurcations are revealed by the rigorous analysis. Finally, numerical simulations are in good agreement with the theoretical analysis. 相似文献
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In this paper, a phytoplankton–zooplankton model with toxic liberation delay is considered. Firstly, the critical values of Hopf bifurcation, transcritical bifurcation and Hopf-transcritical bifurcation are given, and to give more detailed information about the periodic oscillations, the direction and stability of Hopf bifurcation is studied by using the normal-form theory and center manifold theorem. Then, we give the detailed bifurcation set by calculating the universal unfoldings near the Hopf-transcritical bifurcation point. Finally, we show that the plankton system may exhibit quasi-periodic oscillations, which are verified both theoretically and numerically, and explain the experimental observed fluctuation phenomenon of plankton population. 相似文献
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In this paper, we propose a bioeconomic differential algebraic predator–prey model with Holling type II functional response and nonlinear prey harvesting. As the nonlinear prey harvesting is introduced, the proposed model displays a complex dynamics in the predator–prey plane. Taking into account of the economic factor, our predator–prey system is established by bioeconomic differential algebraic equations. The effect of economic profit on the proposed model is analyzed by viewing it as a bifurcation parameter. By jointly using the normal form of differential algebraic models and the bifurcation theory, the stability and bifurcations (singularity induced bifurcation, Hopf bifurcation) are discussed. These results obtained here reveal richer dynamics of the bioeconomic differential algebraic predator–prey model with nonlinear prey harvesting, and suggest a guidance for harvesting in the practical word. Finally, numerical simulations are given to demonstrate the results. 相似文献
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A differential delay equation model with a discrete time delay and a distributed time delay is introduced to simulate zooplankton–nutrient interaction. The differential inequalities’ methods and standard Hopf bifurcation analysis are applied. Some sufficient conditions are obtained for persistence and for the global stability of the unique positive steady state, respectively. It was shown that there is a Hopf bifurcation in the model by using the discrete time delay as a bifurcation parameter. 相似文献
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An SEIR epidemic model with a nonlinear incidence rate is studied. The incidence is assumed to be a convex function with respect
to the infective class of a host population. A bifurcation analysis is performed and conditions ensuring that the system exhibits
backward bifurcation are provided. The global dynamics is also studied, through a geometric approach to stability. Numerical
simulations are presented to illustrate the results obtained analytically. This research is discussed in the framework of
the recent literature on the subject.
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In this paper, we derive a semi-discrete system for a nonlinear model of blood cell production. The local stability of its fixed points is investigated by employing a key lemma from [23, 24]. It is shown that the system can undergo Neimark-Sacker bifurcation. By using the Center Manifold Theorem, bifurcation theory and normal form method, the conditions for the occurrence of Neimark-Sacker bifurcation and the stability of invariant closed curves bifurcated are also derived. The numerical simulations verify our theoretical analysis and exhibit more complex dynamics of this system. 相似文献