共查询到20条相似文献,搜索用时 15 毫秒
1.
Zhang Z.Fu J.Deng G. 《复杂系统与复杂性科学》2015,(1):96-103
Hopf bifurcation behavior and bifurcation control of a new Lorenz-like system are studied in this paper. Firstly, Hopf bifurcation type is determined by bifurcation stability norm. Then the linear controller and the non-linear controller are applied to control the original system respectively. In the section of linear control, the effect of linear parameter on the position of Hopf bifurcation is discussed by Routh-Hurwitz criterion; In the section of non-linear control, the Hopf bifurcation Normal Form of controlled system is obtained by using direct Normal Form method, and the effects of nonlinear parameter on amplitude of limit cycle and Hopf bifurcation type are discussed by coefficient of Normal Form. Discussions show that if non-linear parameter satisfies certain condition, bifurcation type of original system will be changed, and the periodic solution amplitude will increase with the parameter increasing. ©, 2015, The Journal Agency of Complex Systems and Complexity Science. All right reserved. 相似文献
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针对恶意软件在信息物理融合系统中传播机理难以描述的问题,利用非线性动力学理论构建其传播动力学模型,并基于稳定性理论和Hopf分岔定理对该模型的复杂动力学行为进行分析.为了控制恶意软件传播所引发的Hopf分岔,根据分岔控制理论设计了一类结合参数调节法与状态反馈法的混合分岔控制策略,并深入研究控制参数对Hopf分岔点位置及极限环幅值的影响.数值仿真结果表明所设计的混合分岔控制策略不仅能够提前或推迟Hopf分岔点,而且可以改变极限环幅值大小,使信息物理融合系统产生预期的动力学行为,实现控制目的,从而有效降低恶意软件的危害. 相似文献
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Exponential stability of the first order singular distributed parameter systems is discussed in the light of degenerate semi-group methods, which is described by the abstract developing equation in Hilbert space. The necessary and sufficient conditions concerning the exponential stability of the first order singular distributed parameter systems are given. 相似文献
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LIU Zhenrong 《系统科学与复杂性》1992,(4)
In this paper a mathematical model of chemical systems is investigated.We present the conditions for the existence and local stability of the steady statesand the periodic solution of the Hopf type.Specifically,we show by using an ana-lytical method that there may exist two or four Hopf bifurcation points separatedat a finite distance from each other;at the same time,a technique for studying theHopf bifurcation value is given. 相似文献
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井竹君 《系统科学与复杂性》1989,(4)
A predator-prey system,depending on several parameters,is investigated forbifurcation of equilibria,Hopf bifurcation,global bifurcation occurring saddle connection,and global existence and nonexistence of limit cycles,and changes of the topological structureof trajectory as parameters are varied. 相似文献
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The singularly perturbed bifurcation subsystem is described,and the test conditions of subsystem persistence are deduced.By use of fast and slow reduced subsystem model,the result does not require performing nonlinear transformation.Moreover,it is shown and proved that the persistence of the periodic orbits for Hopf bifurcation in the reduced model through center manifold.Van der Pol oscillator circuit is given to illustrate the persistence of bifurcation subsystems with the full dynamic system. 相似文献
7.
The singularly perturbed bifurcation subsystem is described, and the test conditions of subsystem persistence are deduced. By use of fast and slow reduced subsystem model, the result does not require performing nonlinear transformation. Moreover, it is shown and proved that the persistence of the periodic orbits for Hopf bifurcation in the reduced model through center manifold. Van der Pol oscillator circuit is given to illustrate the persistence of bifurcation subsystems with the full dynamic system. 相似文献
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A system of three-unit networks with coupled cells is investigated.The general formula for bifurcation direction of Hopf bifurcation is calculated and the estimate formula of period of the periodic solution is given. 相似文献
9.
数值逼近是数值计算中的基本问题,对仿真算法的理论研究有重要意义.文章研究了一类重要的双时滞神经网络模型的Hopf分支的数值逼近问题.首先,将时滞差分方程表示为映射,然后利用离散动力系统的分支理论,给出了差分方程的Hopf分支存在的条件.得到了连续模型的Hopf分支与其数值逼近的关系.证明了当该模型在juu=(L,2,1=j)处有Hopf分支时,其数值逼近在相应的)(hj=uu(L,2,1=j)处产生Hopf分支.数值Hopf分支值与原连续系统的Hopf分支值之间满足)()(hOhjj =uu. 相似文献
10.
This paper studies a prey-predator singular bioeconomic system with time delay and diffusion, which is described by differential-algebraic
equations. For this system without diffusion, there exist three bifurcation phenomena: Transcritical bifurcation, singularity
induced bifurcation, and Hopf bifurcation. Compared with other biological systems described by differential equations, singularity
induced bifurcation only occurs in singular system and usually links with the expansion of population. When the diffusion
is present, it is shown that the positive equilibrium point loses its stability at some critical values of diffusion rate
and periodic oscillations occur due to the increase of time delay. Furthermore, numerical simulations illustrate the effectiveness
of results and the related biological implications are discussed. 相似文献
11.
CHEN Huaxiong SHEN Jianhe ZHOU Zheyan 《系统科学与复杂性》2014,(6):1158-1171
This paper is concerned with the existence and the analytical approximations of limit cycles in a three-dimensional nonlinear autonomous feedback control system. Based on three-dimensional Hopf bifurcation theorem, the existence of limit cycles is first proved. Then the homotopy analysis method (HAM) is applied to obtain the analytical approximations of the limit cycle and its frequency. In deriving the higher-order approximations, the authors utilized the idea of a perturbation procedure proposed for limit cycles' approximation in van der Pol equation. By comparing with the numerical integration solutions, it is shown that the accuracy of the analytical results obtained in this paper is very high, even when the amplitude of the limit cycle is large. 相似文献
12.
LIN Yiping 《系统科学与复杂性》1995,(2)
DYNAMICALBEHAVIORSOFAFOUR-DIMENSIONALSYSTEMININFECTIOUSDISEASELINYiping(YunnanInstituteofAppliedMathematics,KunmingInstituteo... 相似文献
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不对称非线性蔡氏电路产生的混沌现象分析 总被引:1,自引:0,他引:1
为了更确切地描述实际系统中的混沌现象,提出了一种变形蔡氏电路,它含有一个不对称非线性阻性元件。对该电路进行了深入的数学分析;并在MATLAB环境下,对其产生的混沌现象进行了仿真分析。分析结果表明:改变电路中的线性电阻值R,可以观察到直流平衡态、Hopf分岔、倍周期分岔、单涡卷混沌吸引子、周期性窗口和不对称双涡卷混沌吸引子等非线性动力学行为;混沌系统对初始条件极其敏感;不对称非线性蔡氏电路有其特殊的性质。 相似文献
16.
YUAN Sanling MA Zhien 《系统科学与复杂性》2001,(3)
1 IntroductionFor epidemic model with delays, many people have done a lot of work and many valuableresults have been obtained. In SIS ePidemiologic models, susceptibles become infectious aftersufficieot contact with an infective and then become susceptible again after they have recoveredfrom the infection. SIS models with a time delay in the infectious class and a constan poWulation size were analyzed by Cooke and Yorke[1] and Greenberg and Hoppensteadt[2J. TheyfOund that aJl solutions a… 相似文献
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分析了具有PI控制的Buck变换器中的低频振荡现象。利用离散模型研究了Buck变换器中的低频振荡现象,结果表明系统产生低频振荡的原因是状态变量发生了Hopf分岔。采用状态空间平均的小信号模型分析了变换器的稳定性,它所确定的稳定运行临界点恰好与从离散模型得到的Hopf分岔点的位置相吻合,这表明线性的小信号平均模型可以准确的预测低频振荡的参数稳定域。通过分析发生低频振荡后的频率和幅值,结果表明Buck变换器中的低频振荡现象实际上是一种自激振荡。最后通过数值仿真和电路实验验证了理论分析的合理性。 相似文献
18.
LUO Dingjun 《系统科学与复杂性》1999,(2)
1.IntroductionForagivenunperturbedplanarsystemwithafamilyofclosedorbits,considerthecreationofisolatedclosedorbits--limitcyclesbyperturbationofthesystem.ThatiscalledthePoillcar6bifurcation.Therearewell-knowntheoreticalresultsaboutPoincar6bifllrcati()11,seeforexam-Ple[1],[2].InthecasewheretheunperturbedsystemisHamiltonian,thepertllrbedsystemcanbewrittenasinwhichweassumethatp(x,y,0)=Q(x,U,(i)~0,and(1)A--ohasafamilyofclosedorbitsgivenbytheHamiltonianintegralnfH(x,y)=h,0相似文献
19.
针对传统的城市人口规模演化模型,尤其是Logistic增长型模型所存在的局限性,应用分支理论提出了城市人口规模分支演化模型;并分别对其进行了分支稳定性分析与随机性分析和描述(包括分支概率的极大极小判别以及随机涨落分析);最后将分支模型应用于天津市区人口规模演化的一段历史踪迹的分析,并与Logistic模型进行了对比以说明该模型的优越性和有效性。 相似文献