一类时变非线性振动系统的同步控制方法

对于一类非自治的非线性振动系统，设计了控制方法并建立了相应的派生系统，使得派生系统能与原系统达到同步.利用Lyapunov稳定性理论证明了两个系统在一定条件下可以达到同步，给出了耦合参数的选择条件.对于含参数激励与强迫激励的Mathieu方程以及拟周期激励的Duffing方程进行了实际的仿真计算，证明了派生系统可以与原系统的拟周期、混沌运动快速实现同步. 关键词： 派生系统 同步 差别方程     

单结晶体管二阶RLC串联电路中的周期分岔和混乱运动

本文提出一种新的非线性二阶单结晶体管强迫振荡电路,能在周期激励项参数变动的很大范围内发生倍周期分岔和混乱运动现象。 关键词：     

试样激励下轻敲模式原子力声显微镜的非线性动力学特性

利用Euler-Bernoulli梁理论和DMT针尖-样品作用力模型建立了试样激励下轻敲模式原子力声显微镜(AFAM)系统的动力学方程,并应用非线性动力学分析方法对AFAM微悬臂梁的振动特性进行研究。通过合理改变超声激励幅值、超声激励频率和针尖-样品初始间距等模型参数模拟得到微悬臂梁的超谐波、次谐波、准周期和混沌振动现象,采用时间序列、频谱、相空间、Poincare截面和Lyapunov指数等方法对不同非线性振动特性进行表征。通过分析不同模型参数条件下微悬臂梁针尖-样品作用力特性,探索了微悬臂梁不同非线性振动现象的产生机制。此外,研究了AFAM微悬臂梁运动的分岔特性,发现当超声激励幅值和针尖-样品初始间隙连续变化时,周期、准周期和混沌运动交替出现。研究结果对AFAM系统非线性动力学行为分析和混沌振动控制提供了理论参考。      

含有界随机参数的双势阱Duffing-van der Pol系统的倍周期分岔

讨论简谐激励作用下含有界随机参数的双势阱Duffing-van der Pol系统的倍周期分岔现象.首先用Chebyshev 多项式逼近法将随机Duffing-van der Pol系统化成与其等价的确定性系统，然后通过等价确定性系统来探索该系统的倍周期分岔现象.数值模拟显示随机Duffing-van der Pol 系统与均值参数系统有着类似的倍周期分岔行为，同时指出，随机参数系统的倍周期分岔有其自身独有的特点.文中的主要数值结果表明Chebyshev 多项式逼近法是研究非线性随机参数系统动力学问题的一种有效方法. 关键词： Chebyshev多项式 随机Duffing-van der Pol系统 倍周期分岔     

轴向加速运动黏弹性梁受迫振动中的混沌动力学

研究了黏弹性轴向运动梁在外部激励和参数激励共同作用下横向振动的混沌非线性动力学行为. 引入有限支撑刚度, 并考虑黏弹性本构关系取物质导数, 同时计入由梁轴向加速度引起的沿径向变化的轴力, 建立轴向运动黏弹性梁横向非线性振动的偏微分-积分模型. 通过Galerkin截断方法研究了外部激励的频率和因速度简谐脉动引起的参数激励的频率在不可通约关系时轴向运动连续体的非线性动力学行为, 并对不同截断阶数的数值预测进行了对比. 基于对控制方程的Galerkin截断, 得到离散化的常微分方程组, 使用四阶Runge-Kutta方法求解. 基于此数值解, 运用非线性动力学时间序列分析方法, 通过Poincaré 映射, 观察到轴向运动梁随扰动速度幅值的倍周期分岔现象, 并比较了有无外部激励对倍周期分岔的影响. 分别在低速以及近临界高速运动状态下, 从相平面图、Poincaré 映射以及频谱分析的角度识别了系统中存在的准周期运动形态. 关键词： 轴向运动梁 非线性 混沌 分岔     

一类准周期参激非线性相对转动动力系统的稳定性与时滞反馈控制

建立了一类含准周期参数激励和时滞反馈的相对转动非线性系统的动力学方程. 采用多尺度法求解1/2亚谐波主参数共振下的分岔响应方程,并分析了系统的稳定性. 在求解非受控系统的定常解的基础上,通过讨论系统的动力学特性,研究了准周期参数激励对系统响应的影响. 采用时滞反馈控制的方法对系统分岔和极限环(域)进行控制,数值模拟的结果表明通过改变时滞参数可以实现对系统分岔的控制,并能有效地控制极限环(域)的幅值和稳定性. 关键词： 相对转动 准周期参激 时滞反馈 极限环     

二阶非自治电路中的混沌振荡

本文研究在正弦电源激励下的二阶电路中的非线性动力学性质。在该电路中，唯一的非线性元件是具有负阻特性的单结管，电路实验的结果表明，当改变电源频率时，振荡制式呈现周期递增模式。     

非线性Schroedinger方程的动力学行为分析

采用辛算法数值求解非线性Schroedinger方程的周期初值问题，建立不同的相空间来分忻其动力学持性．首先比较分析了不同的相空间中立方非线性Sehroedinger方程在不同立方非线性参数下的长时间演化的动力学特性，然后讨论了相空间中立方一五次方非线性Sehroedinger方程在不同立方和五次方非线性参数下的长时间演化的动力学特性，数值结果显示，对于不同的立方非线性参数，随着五次方非线性参数的增加，动力学行为的演化路径是不一样的．     

有界噪声与谐和激励联合作用下Duffing-Rayleigh振子的Melnikov混沌

研究了有界噪声与谐和激励作用下的Duffing-Rayleigh振子的动力学行为.首先运用随机Melnikov过程方法得到系统出现混沌的条件,结果表明随着非线性阻尼参数的增加系统会从混沌运动到周期运动,随着Wiener过程强度参数的增加,系统由混沌进入周期的临界幅值会先递增后不变.最后,用两类数值方法即最大Lyapunov指数与Poincare截面验证了上述结果. 关键词： 有界噪声 随机Melnikov过程 混沌运动 周期运动     

基于Chebyshev多项式逼近的随机 van der Pol系统的倍周期分岔分析

应用 Chebyshev 多项式逼近法研究了谐和激励作用下具有随机参数的随机van der Pol系统 的倍周期分岔现象.随机系统首先被转化成等价的确定性系统，然后通过数值方法求得响应 ，借此探索了随机van der Pol系统丰富的随机倍周期分岔现象.数值模拟显示随机van der Pol 系统存在与确定性系统极为相似的倍周期分岔行为，但受随机因素的影响，又有与之不 同之处.数值结果表明，Chebyshev 多项式逼近是研究非线性系统动力学问题的一种新的有 效方法. 关键词： Chebyshev 多项式 随机van der Pol 系统 倍周期分岔     

Self-induced nonlinear spin-orbit interaction of light in liquid crystals

We report on the observation of self-induced nonlinear spin-orbit interaction of light driven by Kerr orientational optical nonlinearities in liquid crystals. It consists of the self-induced spin-to-orbital nonlinear conversion for the angular momentum of light. The optical angular momentum conversion is driven by the creation of a topological liquid crystal defect by the light itself. Moreover, we show that such a nonlinear process can be significantly enhanced by using additional electric fields.     

Absorption-induced optical bistability and dissipative solitons in a BEC interferometer

A model of the absorption-induced nonlinear response of an atomic Bose-Einstein condensate driven by a weak resonant laser beam is presented. The model takes into account the slow BEC decay due to spontaneous emission and magnetic-trap loss by binary collisions, as well as compensation of the decay by injection of ground-state atoms into the trap. It is shown that the nonlinear response is much stronger than in other nonlinear optical media. For a BEC interferometer driven by a monochromatic beam, the threshold intensity for hysteretic switching is found, and dissipative spatial solitons are demonstrated.     

Regular nonlinear response of the driven Duffing oscillator to chaotic time series

Nonlinear response of the driven Duffng oscillator to periodic or quasi-periodic signals has been well studied.In this paper,we investigate the nonlinear response of the driven Duffng oscillator to non-periodic,more specifically,chaotic time series.Through numerical simulations,we find that the driven Duffng oscillator can also show regular nonlinear response to the chaotic time series with different degree of chaos as generated by the same chaotic series generating model,and there exists a relationship between the state of the driven Duffng oscillator and the chaoticity of the input signal of the driven Duffng oscillator.One real-world and two artificial chaotic time series are used to verify the new feature of Duffng oscillator.A potential application of the new feature of Duffng oscillator is also indicated.     

Existence of metastable kinetic modes

The nonlinear evolution of resonantly driven systems, such as suprathermal particle driven modes in magnetically confined plasmas, is shown to strongly depend on the existence and nature of an underlying damping mechanism. When background resonant damping is present, subcritical states can take place. In particular, purely nonlinear steady-state regimes are found, whose destabilization threshold and saturation levels are calculated and validated using numerical simulations. This nonlinear behavior can be of relevance for acoustic modes in magnetically confined plasmas.     

The Mean First-Passage Time for Nonlinear Non-Markovian Continuous Noise

A method for calculating the mean first-passage time for non-Markovian free processes driven by continuous noise is generalized to free process X(t)=g[F(t)] and unfree process X( t)=f[X(t)]g[F(t)] with nonlinear noise. When the switch distribution + rectangular, the exact analytic expressions of the mean first-passage time for free process X(t) = [F(t)]^m driven by nonlinear noise and X( t=) -k[X(t)]ⁿ[F(t)lm+ [F(t)]^m driven by both multiplicative and nonlinear additive noises are also given.     

Homoclinic bifurcation sets of driven nonlinear oscillators

Different quasiperiodically and parametrically driven nonlinear oscillators with quadratic and cubic nonlinearities are considered, and the corresponding homoclinic bifurcation sets in a five-dimensional parameter space are explicitly calculated. We classify all these cases into two basic types of homoclinic bifurcation sets: the first one corresponds to quasiperiodically driven oscillators and the second one corresponds to parametrically driven oscillators.     

Current oscillation and chaotic dynamics in superlattices driven by crossed electric and magnetic fields

We have theoretically studied current oscillation and chaotic dynamics in doped GaAsAlAs superlattices driven by crossed electric and magnetic fields. When the superlattice system is driven by a dc voltage, a stationary or dynamic electric-field domain can be obtained. We carefully studied the electric-field-domain dynamics and current self-oscillation which both display different modes with the change of magnetic field. When an ac electric field is also applied to the superlattice, a typical nonlinear dynamic system is constructed with the ac amplitude, ac frequency, and magnetic field as the control parameters. Different nonlinear behaviors show up when we tune the control parameters.     

Energy transmission in the forbidden band gap of a nonlinear chain

A nonlinear chain driven by one end may propagate energy in the forbidden band gap by means of nonlinear modes. For harmonic driving at a given frequency, the process occurs at a threshold amplitude by sudden large energy flow that we call nonlinear supratransmission. The bifurcation of energy transmission is demonstrated numerically and experimentally on the chain of coupled pendula (sine-Gordon and nonlinear Klein-Gordon equations) and sustained by an extremely simple theory.     

负能模式在驱动漂移波非线性不稳定性中的作用(Ⅱ)——与正能模式交换,“回避交叉”和Hopf分岔

在正弦波驱动的非线性漂移波中,当驱动波频率和强度改变时,一个负能模式与另一个正能模式的复本征值可能出现交叉和“回避交叉”,在出现“回避交叉”的同时,这两个模式的地位发生了某种交换。正负能量两个模式之间的这种非线性共振在弱耗散下可能引起Hopf分岔。     

Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides

We study nonlinear Cerenkov radiation generated from a nonlinear photonic crystal waveguide where the nonlinear susceptibility tensor is modulated by the ferroelectric domain. Nonlinear polarization driven by an incident light field may emit coherently harmonic waves at new frequencies along the direction of Cerenkov angles. Multiple radiation spots with different azimuth angles are simultaneously exhibited from such a hexagonally poled waveguide. A scattering involved nonlinear Cerenkov arc is also observed for the first time. Cerenkov radiation associated with quasi-phase matching leads to these novel nonlinear phenomena.