简并光学参量振荡器混沌反控制

提出一种实现简并光学参量振荡器混沌反控制的方法，用正弦信号调制简并光学参量振荡器的基模衰减率，使简并光学参量振荡器从定态输出转化为混沌态.数值模拟结果表明，选择不同的调制幅度和调制角频率，只要满足系统的最大李雅谱诺夫指数大于零，即可实现不同的混沌轨道重构.通过比较最大李雅谱诺夫指数λ_max随调制幅度和调制角频率变化曲线， 指出系统从周期态调制到混沌态比从无亚谐波输出的定态调制到混沌态更容易，有更宽的调制幅度和调制角频率选择范围. 关键词： 简并光学参量振荡器 混沌反控制 调制     

一种改进的谐振参数扰动法及其在DC/DC变换器混沌控制中的应用

种改进的谐振参数扰动法来控制混沌，该混沌控制方法引入了基于非线性映射的调制，其控制目标可以是任意周期的轨道，而不是原混沌吸引子中的嵌入轨道。作为一个应用实例，文中描述了该方法在电流模式控制dc/dc变换器中的应用结果。     

玻色-爱因斯坦凝聚系统中原子的空间混沌分布

研究了非对称周期势阱中玻色-爱因斯坦凝聚原子的空间混沌分布结构. 在凝聚体相位为常数的情况下, 凝聚体内部不存在原子流,凝聚原子的空间分布结构可以用一个无阻尼双驱动Duffing方程描述. 理论分析给出了原子间呈排斥作用系统的Mel'nikov混沌判据.数值模拟结果显示,化学势的增大能够对原子混沌分布产生明显的抑制作用,甚至使混沌完全消失. 对于原子间呈吸引作用的系统,在一定参数条件下,调节光格势强度比可以使凝聚原子由周期状态进入到空间混沌分布状态,随着化学势的增大这种空间混沌分布被完全抑制. 关键词： 玻色-爱因斯坦凝聚 Mel'nikov函数 混沌     

玻色-爱因斯坦凝聚中的混沌反控制

提出一种实现玻色-爱因斯坦凝聚中的混沌反控制方法——周期信号驱动法.数值模拟结果表明,用小的周期信号控制系统,采用恰当的调制相位和强度,只要满足系统的最大Lyapunov指数大于零即可实现不同的混沌轨道重构.调制相位在混沌轨道重构中起了很重要的作用. 关键词： 玻色-爱因斯坦凝聚 混沌反控制 小周期信号 Lyapunov指数     

Suppressing chaos by parametric perturbation at doubled frequency of periodic perturbation

An analysis of the chaos suppression of a nonlinear elastic beam(NLEB)is presented.In terms of modal transformation the equation of NLEB is reduced to the Duffing equation.It is shown that the chaotic behaviour of the NLEB is sensitively dependent on the parameters of perturbations and initial conditions.By adjusting the frequency of parametric perturbation to twice that of the periodic one and the amplitude of parametric pertubation to the same as the periodic one,the chaotic region of the nonlinear elastic beam driven by periodic force can be greatly suppressed.     

双频激励下超晶格系统的混沌行为

假设超晶格“折沟道”对粒子的作用等效为形状相似的周期调制; 引入正弦平方势, 在小振幅近似下, 把粒子运动方程化为具有双频激励的Duffing方程。 用Melnikov方法分析了系统的混沌行为。 结果表明, 当外场为双频激励时, 系统将存在不同的次谐和超次谐分叉序列。 由于系统的混沌行为与系统参数有关, 于是, 只需控制材料组分、 或掺杂浓度, 就可望达到避免或控制混沌的目的, 为半导体超晶格的制备及其光磁电效应提供了理论分析。     

Anti-control of chaos in Bose-Einstein condensates

The spatial structure of a Bose-Einstein Condensate (BEC) loaded into an optical lattice potential is investigated. We suggest a method for generating chaos in BEC by modulating periodic signals to convert the regular states into chaotic states. The maximal Lyapunov exponent is calculated as a function of modulation intensity and modulation frequency respectively, and the chaotic orbits associated with the positive Lyapunov exponents.      

Intermittent lag synchronization in a nonautonomous system of coupled oscillators

Synchronization properties of two identical mutually coupled Duffing oscillators with parametric modulation in one of them are studied. Intermittent lag synchronization is observed in the vicinity of saddle-node bifurcations where the system changes its dynamical state. This phenomenon is seen as intermittent jumps from phase to lag synchronization, during which the chaotic trajectory visits closely a periodic orbit. Different types of intermittent lag synchronization are demonstrated and the simplest case of period-one lag synchronization is analyzed.     

Instability control in microwave-frequency microplasma

This paper introduces comprehensive large-signal analyses of modulation dynamics and noise of a chaotic semiconductor laser. The chaos is induced by operating the laser under optical feedback (OFB). Control of the chaotic dynamics and possibility of suppressing the associated noise by sinusoidal modulation are investigated. The studies are based on numerical solutions of a time-delay rate equation model. The deterministic modulation dynamics of the laser are classified into seven regular and irregular dynamic types. Variations of chaotic dynamics and noise with sinusoidal modulation are examined in both time and frequency domains over wide ranges of the modulation depth and frequency. The results showed that chaotic dynamics can be converted into five distinct dynamic types; namely, continuous periodic signal (CPS), continuous periodic signal with relaxation oscillations (CPSRO), periodic pulse (PP), periodic pulse with relaxation oscillations (PPRO) and periodic pulse with period doubling (PPPD). The relative intensity noise (RIN) of these types is characterized when the modulation frequencies are much lower, comparable to, and higher than the resonance frequency. Suppression of RIN to a level 8 dB/Hz higher than the quantum limit was predicted under the CPS type when the modulation frequency is 0.9 times the resonance frequency and the modulation depth is 0.14.     

Intermittent lag synchronization in a driven system of coupled oscillators

We study intermittent lag synchronization in a system of two identical mutually coupled Duffing oscillators with parametric modulation in one of them. This phenomenon in a periodically forced system can be seen as intermittent jump from phase to lag synchronization, during which the chaotic trajectory visits a periodic orbit closely. We demonstrate different types of intermittent lag synchronizations, that occur in the vicinity of saddle-node bifurcations where the system changes its dynamical state, and characterize the simplest case of period-one intermittent lag synchronization.     

Numerical experiments of the planar equal-mass three-body problem: the effects of rotation

The planar three-body problem with angular momentum is numerically and systematically studied as a generalization of the free-fall problem (i.e., the three-body problem with zero initial velocities). The initial conditions in the configuration space exhaust all possible forms of a triangle, whereas the initial conditions in the momentum space are chosen so that position vectors and momentum vectors are orthogonal. Numerical results are organized according to the value of virial ratio k defined as the ratio of the total kinetic energy to the total potential energy. Final motions are mapped in the initial value space. Several interesting features are found. Among others, binary collision curves seem to spiral into the Lagrange point, and for large k, binary collision curves connect the Lagrange point and the Euler point. The existence of a lunar periodic orbit and a periodic orbit of petal-type is suggested. The number of escape orbits as a function of the escape time is analyzed for different k. The behavior of this number for different time and k shows most remarkably the effects of rotation of triple systems. The number of escape orbits increases exponentially for k相似文献   

On the dynamics of a two-mode laser with periodically modulated parameter

The results for a numerical simulation of a two-mode homogeneously-broadened laser due to a periodic pump modulation are presented. The region with the parameters for the complicated periodic and chaotic laser-intensities pulsation to be observed has also been defined. Complex bifurcation diagram versus modulation frequency with the periodic and chaotic regimes alternation is presented.     

GENERAL SYNCHRONIZATION OF CHAOS IN A SYSTEM OF TWO NON-IDENTICAL LASERS

General synchronization of the chaotic intensity fluctuations of two spatially coupled Nd:YAG lasers with pump modulation is investigated theoretically when the losses of the two lasers are different. It is shown that the chaotic synchronization still exists for medium coupling even though the two lasers are different. For strong coupling the system shows periodic motion of laser intensities. While for weak coupling, the two lasers oscillate independently. It is obvious that the increase of difference between the two lasers reduces the degree of chaotic synchronization.     

Slowly rocking symmetric, spatially periodic Hamiltonians: The role of escape and the emergence of giant transient directed transport

The nonintegrable Hamiltonian dynamics of particles placed in a symmetric, spatially periodic potential and subjected to a periodically varying field is explored. Such systems can exhibit a rich diversity of unusual transport features. In particular, depending on the setting of the initial phase of the drive, the possibility of a giant transient directed transport in a symmetric, space-periodic potential when driven with an adiabatically varying field arises. Here, we study the escape scenario and corresponding mean escape times of particles from a trapping region with the subsequent generation of a transient directed flow of an ensemble of particles. It is shown that for adiabatically slow inclination modulations the unidirectional flow proceeds over giant distances. The direction of escape and, hence, of the flow is entirely governed whether the periodic force, modulating the inclination of the potential, starts out initially positive or negative. In the phase space, this transient directed flow is associated with a long-lasting motion taking place within ballistic channels contained in the non-uniform chaotic layer. We demonstrate that for adiabatic modulations all escaping particles move ballistically into the same direction, leading to a giant directed current.     

Model for modulated and chaotic waves in zero-Prandtl-number rotating convection

The effects of time-periodic forcing in a few-mode model for zero-Prandtl-number convection with rigid body rotation is investigated. The time-periodic modulation of the rotation rate about the vertical axis and gravity modulation are considered separately. In the presence of periodic variation of the rotation rate, the model shows modulated waves with a band of frequencies. The increase in the external forcing amplitude widens the frequency band of the modulated waves, which ultimately leads to temporally chaotic waves. The gravity modulation, on the other hand, with small frequencies, destroys the quasiperiodic waves at the onset and leads to chaos through intermittency. The spectral power density shows more power to a band of frequencies in the case of periodic modulation of the rotation rate. In the case of externally imposed vertical vibration, the spectral density has more power at lower frequencies. The two types of forcing show different routes to chaos.      

Controlling chaos based on an adaptive nonlinear compensator mechanism

The control problems of chaotic systems are investigated in the presence of parametric uncertainty and persistent external disturbances based on nonlinear control theory. By using a designed nonlinear compensator mechanism, the system deterministic nonlinearity, parametric uncertainty and disturbance effect can be compensated effectively. The renowned chaotic Lorenz system subjected to parametric variations and external disturbances is studied as an illustrative example. From the Lyapunov stability theory, sufficient conditions for choosing control parameters to guarantee chaos control are derived. Several experiments are carried out, including parameter change experiments, set-point change experiments and disturbance experiments. Simulation results indicate that the chaotic motion can be regulated not only to steady states but also to any desired periodic orbits with great immunity to parametric variations and external disturbances.     

A semi-dissipative crisis

This article reports a sudden chaotic attractor change in a system described by a conservative and dissipative map concatenation. When the driving parameter passes a critical value, the chaotic attractor suddenly loses stability and turns into a transient chaotic web. The iterations spend super-long random jumps in the web, finally falling into several special escaping holes. Once in the holes, they are attracted monotonically to several periodic points. Following Grebogi, Ott, and Yorke, we address such a chaotic attractor change as a crisis. We numerically demonstrate that phase space areas occupied by the web and its complementary set (a fat fractal forbidden net) become the periodic points' “riddled-like” attraction basins. The basin areas are dominated by weaker dissipation called “quasi-dissipation”. Small areas, serving as special escape holes, are dominated by classical dissipation and bound by the forbidden region, but only in each periodic point's vicinity. Thus the crisis shows an escape from a riddled-like attraction basin. This feature influences the approximation of the scaling behavior of the crisis's averaged lifetime, which is analytically and numerically determined as 〈τ〉∝(b-b₀)^γ, where b₀ denotes the control parameter's critical threshold, and γ≃-1.5.     

周期参数扰动的T混沌系统同宿轨道分析

针对一类周期参数扰动的T混沌系统, 通过变换将系统转化为具有广义Hamilton结构的周期参数扰动的慢变系统, 运用Melnikov方法对系统的同宿轨道进行了分析计算, 并给出了系统的同宿轨道参数分支条件. 同时, 通过数值实验, 对周期参数扰动控制策略及同宿轨道进行了仿真, 验证了文中理论分析的正确性. 关键词： Hamilton系统 Melnikov方法 同宿轨道 周期参数扰动     

The benefits of multibit chaotic sigma delta modulation

Sigma delta modulation is a popular technique for high-resolution analog-to-digital conversion and digital-to-analog conversion. We investigate chaotic phenomena in multibit first-order sigma-delta modulators. Particular attention is placed on the occurrence of periodic orbits or limit cycles. These may result in idle tones audible to the listener when sigma-delta modulation is used for audio signal processing. One suggested method of eliminating idle tones is the operation of a sigma delta modulator in the chaotic regime. Unfortunately, chaotic modulation of a first order sigma delta modulator is a poor system for signal processing. We show that minor variations on a traditional first order sigma-delta modulator, together with a multibit implementation, may be used to produce an effective, stable chaotic modulator that accurately encodes the input and helps remove the presence of idle tones. (c) 2001 American Institute of Physics.     

Suppression of chaotic oscillations in a microchip laser by injection of a new orbit into the chaotic attractor

Suppression of chaotic instability arising in a Nd:YVO(4) microchip laser subject to frequency-shifted optical feedback is accomplished by injection of one of the periodic orbits into the bifurcation region of another chaotic system driven by pump modulation. Various periodic patterns, which do not exist in the original chaotic attractor, can be extracted from the chaotic oscillation by use of this nonfeedback chaos-control technique.