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1.
Hopf bifurcation and chaos of a nonlinear electromechanical coupling relative rotation system are studied in this paper. Considering the energy in air-gap field of AC motor, the dynamical equation of nonlinear electromechanical coupling relative rotation system is deduced by using the dissipation Lagrange equation. Choosing the electromagnetic stiffness as a bifurcation parameter, the necessary and sufficient conditions of Hopf bifurcation are given, and the bifurcation characteristics are studied. The mechanism and conditions of system parameters for chaotic motions are investigated rigorously based on the Silnikov method, and the homoclinic orbit is found by using the undetermined coefficient method. Therefore, Smale horseshoe chaos occurs when electromagnetic stiffness changes. Numerical simulations are also given, which confirm the analytical results.  相似文献   

2.
陈向炜 《中国物理》2002,11(5):441-444
Chaotic behaviour in a second-order autonomous Birkhoff system with a heteroclinic circle under weakly periodic perturbation is studied using the Melnikov method.The equations of heteroclinic orbits and the criteria for chaos are given.One example is also presented to illustrate the application of the results.  相似文献   

3.
We demonstrate a method for controlling strong chaos by an aperiodic perturbation in two-dimensional Hamiltonian systems.The method has the advantages that the controlled system remains conservative property and the selection of the perturbation has a considerable diversity.We illustrate this method with two area preserving maps:the non-monotonic twist map which is a mixed system and the perturbed cat map which exhibits hard chaos.Numerical results show that the strong chaos can be effectively controlled into regular motions,and the final states are always quasiperiodic ones.The method is robust against the presence of weak external noise.  相似文献   

4.
潘伟珍  宋向炯  俞军 《中国物理 B》2010,19(3):30203-030203
The dynamical behaviour of the generalized Korteweg-de Vries(KdV) equation under a periodic perturbation is investigated numerically.The bifurcation and chaos in the system are observed by applying bifurcation diagrams,phase portraits and Poincar maps.To characterise the chaotic behaviour of this system,the spectra of the Lyapunov exponent and Lyapunov dimension of the attractor are also employed.  相似文献   

5.
刘利伟  谭磊  黄刚 《中国物理 B》2011,20(1):14205-014205
A theoretical study is carried out for the modification and implication of the effect on the Ξ-type three level atom in a high-finesse optical cavity driven by light field including spontaneous emission and the cavity decay. Analytic expressions for the dipole force, the friction force, the optical potentials and the friction coefficient are obtained. Then the numerical and graphical methods are used to investigate the friction coefficient with the controlling parameters. It is shown that the friction coefficient is strongly dependent on the controlling parameters. The cooling rate can increase by one order of magnitude more than that of a two-level atomic system. The reason can be given using the dressed states and the Sisyphus cooling mechanism, which would stimulate further experimental investigations.  相似文献   

6.
A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonie model of a two-dimensional oscillator having Kratzer potential energy function is used to model the molecular species and to represent the unperturbed system. A selection rule for the radial quantum number of the oscillator is derived. The eigenfunctions of a two-dimensional anharmonic oscillator in cylindrical coordinates are used for the matrix elements representing the probability for energy transitions in dipole approximation to be calculated. Several forms of perturbation operators are proposed to model the interaction between the polyatomic molecular species and an electrostatic field. It is found that the degeneracy is removed in the presence of the electric field and spectral splitting occurs. Anharmonic approximation for the unperturbed system is more accurate and reliable representation of a reaJ polyatomic molecular species.  相似文献   

7.
在经典力学框架内和偶极近似下,引入正弦平方势,把粒子运动方程化为具有阻尼项和受迫项的广义摆方程。利用Melnikov方法讨论了沟道运动次谐分叉及其稳定性, 导出了周期弯晶的临界条件和退道长度。结果表明, 要试图获得高的引出效率, 除了要求弯晶长度必须小于退道长度外, 还必须保证沟道粒子的运动是稳定的。对临界条件的分析表明, 系统的稳定性与它的参数有关, 只须适当调节系统参数, 就可以保证周期弯晶作为引出元件的稳定性。In the classical mechanics frame and with a dipole approximation the particle motion equation in the periodic bent crystal is reduced to the general pendulum equation with a damping term and the forced term by using the sine squared potential. This paper discusses the problem of the sub harmonic bifurcation of the periodic orbit and the stabilities of the channeling motion by using Melnikov method, so as to derive the critical condition and the dechanneling length of the periodic bent crystal. The results show that channeling motion must be stable in addition that the crystal length is smaller than the dechanneling length in order to ensure higher extracted efficiency. The analysis of the critical condition shows that the system stabilities are related to its parameters. Just by properly regulating the parameters of the system, the dynamic stabilities by the use of periodic bent crystal as beam control cell can be ensured.  相似文献   

8.
This article introduces a new chaotic system of three-dimensional quadratic autonomous ordinary differential equations, which can display different attractors with two unstable equilibrium points and four unstable equilibrium points respectively. Dynamical properties of this system are then studied. Furthermore, by applying the undetermined coefficient method, heteroclinic orbit of Shil'nikov's type in this system is found and the convergence of the series expansions of this heteroclinic orbit are proved in this article. The Shil'nikov's theorem guarantees that this system has Smale horseshoes and the horseshoe chaos.  相似文献   

9.
The temporal evolution of the degree of entanglement between two atoms in a system of the binomial optical field interacting with two arbitrary entangled atoms is investigated. The influence of the strength of the dipole–dipole interaction between two atoms, probabilities of the Bernoulli trial, and particle number of the binomial optical field on the temporal evolution of the atomic entanglement are discussed. The result shows that the two atoms are always in the entanglement state. Moreover, if and only if the two atoms are initially in the maximally entangled state, the entanglement evolution is not affected by the parameters, and the degree of entanglement is always kept as 1.  相似文献   

10.
The dynamics of a Josephson junction array shunted by a common resistance are investigated by using numerical methods. Coexistence of phase locking and chaos is observed in the system when the resistively and capacitively shunted junction model is adopted. The corresponding parameter ranges for phase locking and chaos are presented. When there are three resistively shunted junctions in the array, chaos is found for the first time and the parameter range for chaos is also presented. According to the theory of Chernikov and Schmidt, when there are four or more junctions in the array, the system exhibits chaotic behavior. Our results indicate that the theory of Chernikov and Schmidt is not exactly appropriate.  相似文献   

11.
《Physics letters. A》2006,355(2):104-109
We investigate the chaotic phase oscillation of a proton beam in a cooler synchrotron. By using direct perturbation method, we construct the general solution of the 1st-order equation. It is demonstrated that the general solution is bounded under some initial and parameter conditions. From these conditions, we get a Melnikov function which predicts the existence of Smale-horseshoe chaos iff it has simple zeros. Our result under the 1st-order approximation is in good agreement with that in [H. Huang et al., Phys. Rev. E 48 (1993) 4678]. When the perturbation method is not suitable for the system, numerical simulation shows the system may present transient chaos before it goes into periodical oscillation; changing the damping parameter can result in or suppress stationary chaos.  相似文献   

12.
一维晶化束的非线性动力学(Ⅱ)   总被引:5,自引:0,他引:5       下载免费PDF全文
本文导出了参数激励的横向相干振动方程。用多重尺度法求出了系统的近似解,用经典方法讨论了它的稳定性,导出了系统的临界梯度场公差和频率响应曲线。此外,还利用Melni-kov方法讨论了系统的全局分叉并以储存环ESR为例进行了详细分析。 关键词:  相似文献   

13.
In this study, we propose a remarkably simple oscillator that exhibits extremely complicated behaviors. The second-order nonautonomous differential equation discussed in this Letter is considered to be one of the simplest dynamics that can produce mixed-mode oscillations (MMOs) and chaos. Our model uses a Bonhoeffer-van der Pol (BVP) oscillator under weak periodic perturbation. The parameter set of the BVP equation is chosen such that a focus and a relaxation oscillation coexist when no perturbation is applied. Under weak periodic perturbation, various types of MMOs and chaos with remarkably complicated waveforms are observed.  相似文献   

14.
微波管中离子张弛振荡引起的噪声对其工作性能有很大影响,已成为微波管领域研究的焦点之一.用包络方程描述电子束特性,用离散的宏粒子模型描述离子特性,在此基础上编写了一维粒子模拟程序,对行波管与速调管模拟,得到张弛振荡的时间序列;将振荡看作是一个复杂非线性动力学系统的响应,分析了离子张弛振荡时间序列的功率谱、重构相图及Lyapunov指数,指出离子张弛振荡具有混沌性质,为研究离子张弛振荡的控制与带有离子振荡噪声信号的处理提供了参考. 关键词: 张弛振荡 粒子模拟 微波管 混沌  相似文献   

15.
一类非自治位置时滞反馈控制系统的亚谐共振响应   总被引:2,自引:0,他引:2       下载免费PDF全文
王洪坡  李杰 《物理学报》2007,56(5):2504-2516
研究了弹性轨道条件下,控制回路中位置反馈信号存在时滞的磁浮系统在亚谐轨道激励作用下的响应问题. 将动力学模型在平衡点处线性化,以时滞为分岔参数,得到了系统出现Hopf分岔的条件. 用中心流形约化方法得到了包含轨道扰动系统的Poincaré规范型. 用多尺度法从理论上推导了时滞磁浮系统的亚谐共振周期解,得到了自由振动的分岔响应方程,分析了周期解中自由振动项的存在条件,研究了控制参数和激励参数与周期解的关系. 最后用数值仿真的方法分析了时滞参数、控制参数对系统响应的影响,分析结果指出,使系统保持稳定的亚谐响应的时滞边界小于无扰动时的时滞边界,时滞参数不但可以抑制亚谐响应,还能够控制混沌的产生,而控制参数可以控制系统响应中自由振动项的出现和受迫振动的幅值,适当选择这些参数可以有效抑制亚谐振动响应. 关键词: 亚谐共振响应 位置时滞反馈控制 非自治磁浮系统 分岔  相似文献   

16.
A hydrodynamic approximation is used to study the behavior of dipole modes of the transverse oscillations of an ion beam in a storage ring with an electron cooling section. It is shown that in addition to the finite interaction time of the beams, instability may be caused by a specific interaction effect between the ion and electron beams in the magnetic field which leads to redistribution of energy between the various modes of the ion beam oscillations. In this case, the condition that the determinant of the transfer matrix for the cooling section does not exceed unity no longer guarantees the stability of the transverse coherent oscillations of the ion beam and all the eigenvalues of the complete matrix of the ion motion including the storage ring must be analyzed. Calculations of the stability of ion beam dipole oscillations are presented for the parameters of CELSIUS.  相似文献   

17.
李明  邵明珠  罗诗裕 《发光学报》2009,30(2):147-151
掺杂超晶格是对同一材料交替掺入n-型和p-型杂质,形成n-i-p-i-n-i-p-i…一维阵列的周期结构。由于交替掺杂,衬底材料的导带受到周期调制形成一个个十分类似于正弦平方形式的量子阱。引入正弦平方势,在经典力学框架内,把粒子的运动方程化为具有阻尼项和受迫项的广义摆方程。用Jacobian椭圆函数和第一类全椭圆积分找到了无扰动系统的解和粒子振动周期,利用Melnikov方法分析了系统的全局分叉与Smale马蹄变换意义上的混沌行为,给出了系统通过级联分叉进入混沌的临界值。结果表明,对于异宿轨道,当参数满足条件 <πsech 时,系统出现了Smale马蹄变换意义上的混沌振荡。对于振荡型周期轨道,当参数满足条件 <πsech 时,产生了奇阶振荡型次谐分叉。注意到系统进入混沌的临界条件与它的参数有关,只需适当调节这些参数就可以避免或控制混沌,为光学双稳态器件的设计提供了理论分析。  相似文献   

18.
Looking for new light sources, especially short wavelength laser light sources has attracted widespread attention. This paper analytically describes the radiation of a crystalline undulator field by the sine-squared potential. In the classical mechanics and the dipole approximation, the motion equation of a particle is reduced to a generalized pendulum equation with a damping term and a forcing term. The bifurcation behavior of periodic orbits is analyzed by using the Melnikov method and the numerical method, and the stability of the system is discussed. The results show that, in principle, the stability of the system relates to its parameters, and only by adjusting these parameters appropriately can the occurrence of bifurcation be avoided or suppressed.  相似文献   

19.
This paper outlines our studies of bifurcation, quasi-periodic road to chaos and other dynamic characteristics in an external-cavity multi-quantum-well laser with delay optical feedback. The bistable state of the laser is predicted by finding theoretically that the gain shifts abruptly between two values due to the feedback. We make a linear stability analysis of the dynamic behavior of the laser. We predict the stability scenario by using the characteristic equation while we make an approximate analysis of the stability of the equilibrium point and discuss the quantitative criteria of bifurcation. We deduce a formula for the relaxation oscillation frequency and prove theoretically that this formula function relates to the loss of carriers transferring between well regime and barrier regime, the feedback level, the delayed time and the other intrinsic parameters. We demonstrate the dynamic distribution and double relaxation oscillation frequency abruptly changing in periodic states and find the multi-frequency characteristic in a chaotic state. We illustrate a road to chaos from a stable state to quasi-periodic states by increasing the feedback level. The effects of the transfers of carriers and the escaping of carriers on dynamic behavior are analyzed, showing that they are contrary to each other via the bifurcation diagram. Also,we show another road to chaos after bifurcation through changing the linewidth enhancement factor, the photon loss rate and the transfer rate of carriers.  相似文献   

20.
A simple model for a distributed self-oscillatory system with cubic nonlinearity and delay is presented. Conditions for oscillation self-excitation and stationary oscillation conditions, as well as the stability of the oscillations, are analyzed. Nonstationary self-modulation regimes (including conditions of complex dynamics and chaos) are simulated numerically over a wide range of control parameters. As the factor of nonequilibrium grows, regular and chaotic regimes alternate in a complex manner. The transitions to chaos may follow all scenarios known for finite-dimensional systems. The model suggested is somewhat akin to a number of earlier finite-dimensional models aimed at studying mode competition in resonance electron masers.  相似文献   

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