Controlling bistability by linear augmentation

In many bistable oscillating systems only one of the attractors is desired to possessing certain system performance. We present a method to drive a bistable system to a desired target attractor by annihilating the other one. This shift from bistability to monostability is achieved by augmentation of the nonlinear oscillator with a linear control system. For a proper choice of the control function one of the attractors disappears at a critical coupling strength in an control-induced boundary crisis. This transition from bistability to monostability is demonstrated with two paradigmatic examples, the autonomous Chua oscillator and a neuronal system with a periodic input signal.     

Detection of global and local parameter variations using nonlinear feedback auxiliary signals and system augmentation

Recently, system augmentation has been combined with nonlinear feedback auxiliary signals to provide sensitivity enhancement in both linear and nonlinear systems. Augmented systems are higher dimensional linear systems that follow trajectories of a nonlinear system one at a time. These augmented systems are subject to a specialized augmented forcing which enforces the augmented system to exactly reproduce the trajectory of the nonlinear system when projected onto the lower dimensional (physical) system. Augmented systems have additional benefits outside of handling nonlinear systems, which makes them more desirable than regular linear systems for sensitivity enhancing control. One of the key advantages of augmented systems is the complete control over the augmented degrees of freedom, and the additional sensor-type knowledge from the augmented variables. These sensing and actuation features are very useful when only few physical actuators and sensors can be placed. Such restrictions are common in most applications, and they severely limit the usefulness of traditional linear sensitivity enhancing feedback approaches. Another benefit of the augmentation is that the control exerted on the augmented degrees of freedom does not require any physical energy, rather it is just signal processing. In this work, these benefits are refined to improve the robustness of detection using sensitivity enhancement. Also, the benefits of system augmentation are explored by using few actuators and sensors. An optimization algorithm is employed not only to maximize the sensitivity of resonant frequencies to added mass at particular locations, but also to detect uniform changes in mass and stiffness. In addition to increased sensitivity for both global and local parameter changes, a study of increasing the sensitivity of local changes, while decreasing the sensitivity of global changes is conducted. Additionally, a methodology is presented to accurately extract augmented frequencies from displacement and forcing data corrupted by noise. Numerical simulations of cantilevered beams are used to validate the approach and discuss the effects of noise.     

Optical bistability and multistability via amplitude and phase control in a Duplicated two-level system

We investigate the optical bistability(OB) in a duplicated two-level system contained in a ring cavity.The atoms are driven by two orthogonally polarized fields with a relative phase.The OB behavior of such a system can be controlled by the amplitude and the relative phase of the coupling field,and it is possible to switch between bistability and multistability by adjusting the relative phase.     

Controlling the optical bistability and multistability in a two-level pumped-probe system

We study the behavior of the optical bistability (OB) and multistability (OM) in a two-level pumped-probe atomic system by means of a unidirectional ring cavity. We show that the optical bistability in a two-level atomic system can be controlled by adjusting the intensity of the pump field and the detuning between two fields. We find that applying the pumping field decreases the threshold of the optical bistability.     

含一个非线性项混沌系统的线性控制及反控制

研究了一类仅含一个非线性项混沌系统的线性控制与反控制,根据Routh-Hurwitz稳定性条件,先对这类混沌系统进行控制,使其达到稳定的状态,然后改变控制系数,使其再次产生混沌,得到一个新的混沌系统,并对这个新的混沌系统的基本动力学行为进行了分析,数值仿真也验证了新系统的混沌性态.     

非共振条件下∧型三能级原子系统光学双稳态和多稳态的控制

非共振条件下,我们理论研究了单向环形光腔中用一微波场驱动一个超精细低能态跃迁的∧型三能级原子系统光学双稳态和多稳态行为,结果表明原子介质双稳态的行为可以分别通过耦合场的强度和耦合场频率的失谐量控制,同时还发现微波场在实现多稳态过程中所起的重要作用.最后讨论了合作参数对光学多稳态阈值的影响.     

Controlling the optical bistability beyond the multi-photon resonance condition in a three-level closed-loop atomic system

We investigate the optical bistability behavior of a three-level closed-loop atomic system beyond the multi-photon resonance condition. Using the Floquet decomposition, we solve the time-dependent equations of motion, beyond the multi-photon resonance condition. By identifying the different scattering processes contributing to the medium response, it is shown that in general the optical bistability behavior of the system is not phase-dependent. The phase dependence is due to the scattering of the driving and coupling fields into the probe field at a frequency, which, in general, differs from the probe field frequency.     

Dynamical hysteresis in a three-level atomic system

We have experimentally investigated dynamical hysteresis behavior by changing the sweeping frequency of the cavity input field in the optical bistability of rubidium atoms (in a three-level atomic-type configuration) inside an optical cavity. The shape, width (or area), and direction of the hysteresis cycle are sensitive functions of the sweeping frequency for such an optical bistable system.     

色散对单模激光系统非线性效应的影响

研究在强光场的作用下 ,激光系统中的腔内介质的折射率不再是常数而引起的非线性效应 ,即色散型激光系统的动力学行为。研究结果表明 ,这类系统的输出场会呈现双稳态 ,并利用极值法确定了描述这类色散型激光系统的Maxvell- bloch方程是现双稳态的参数临界点和双稳态区域     

吸收型双光子光学双稳态的时间行为

利用多重时间尺度微扰分析方法,研究了一个半经典吸收型双光子光学双稳系统的时间演化行为。一级近似结果表明,在高透射分支附近,系统的长时间行为由输出场振幅的方程所支配,其它动力学量除绝热地跟随场振幅变化而外,还有快速振荡。而在低透射分支附近,所有动力学变量都通过长时间尺度变化,没有与短时间尺度相联系的振荡行为。稳定态在高透射分支与低透射分支之间的跃变可以由简单的方程描述。 关键词：     

三维四翼广义增广Lü系统

增广Lü系统是仅含有两个控制参数的三维混沌系统,可产生一个伪四翼吸引子.利用混沌反控制方法,通过在增广Lü系统中引入一个简单的线性状态控制器,提出了一个新三维混沌系统——广义增广Lü系统.新系统实现了一个真正的具有复合结构的四翼吸引子,它包含了两个镜像对称的子系统.理论分析、数值仿真和电路实验证明了广义增广Lü系统四翼吸引子的存在性,也阐述了广义增广Lü系统有着较增广Lü系统更加丰富的动力学特性. 关键词： 广义增广Lü系统 四翼吸引子 数值仿真 电路实验     

Cluster synchronization in fractional-order complex dynamical networks

Cluster synchronization of complex dynamical networks with fractional-order dynamical nodes is discussed in the Letter. By using the stability theory of fractional-order differential system and linear pinning control, a sufficient condition for the stability of the synchronization behavior in complex networks with fractional order dynamics is derived. Only the nodes in one community which have direct connections to the nodes in other communities are needed to be controlled, resulting in reduced control cost. A numerical example is presented to demonstrate the validity and feasibility of the obtained result. Numerical simulations illustrate that cluster synchronization performance for fractional-order complex dynamical networks is influenced by inner-coupling matrix, control gain, coupling strength and topological structures of the networks.     

Optical bistability in a defect slab with a negative refractive quantum dot nanostructure

We demonstrate optical bistability (OB) in a defect slab doped V-type four-level InGaN/GaN quantum dot nanostructure in the negative refraction frequency band. It has been shown that the OB behavior of such a quantum dot nanostructure system can be controlled by the amplitude of the driving fields and a new parameter for controlling the OB behavior as thickness of the slab medium in the negative refraction band. Meanwhile, we show that the negative refraction frequency band can be controlled by tuning electric permittivity and magnetic permeability by the amplitude of the driving fields and electron concentration in the defect slab doped. Under the numerical simulations, due to the effect of quantum coherence and interference, it is possible to switch bistability by adjusting the optimal conditions in the negative refraction frequency band, which is more practical in all-optical switching or coding elements, and technology based nanoscale devices.     

压缩真空注入对光学双稳的影响

研究了注入压缩真空对介质为Ａ－型三能级原子的环形腔的双稳行为的影响。结果表明,压缩真空的注入明显增大了双稳迟滞环。可以注入适当的压缩真空来控制双稳。     

On the presence of spatial pattern formation in a bistable dynamical system

The aim is to investigate whether in a structural bistable reaction-diffusion system pattern formation may emerge simultaneously from both steady states. Therefore, a dynamical system is modelled by three coupled nonlinear differential equations from which synergetic ordering may arise. In addition, the nonlinear terms are chosen such that the homogeneous system is governed by the canonical form of a cusp bifurcation in a two-dimensional control space. Thus, structural bistability is established. Based on a linear stability analysis the region of bistability is decomposed into four different domains in the control plane. It is shown that in one of these domains self-organization can lead to pattern formation from both steady states simultaneously. In two other domains self-organization can arise from only one steady state and finally in one domain patterning is impossible. An expression for the wavelength of a spatial structure is derived and discussed in terms of parameters of the system. As a possible application of the present results a crystal under irradiation with particles of high energy is considered. It is demonstrated for the case of steel that the parameters of the system can be chosen such that a two-fold spatial instability for irradiation induced cavities may emerge.     

Ultra-Low Threshold Optical Bistability and Multi-Stability in Dielecrtric Slab Doped with Semiconductor Quantum Well

A scheme for switching of the optical bistability (OB) and multi-stability (OM) in a dielectric slab doped with a three-level ladder-configuration n-doped semiconductor quantum well is simulated. It is shown that the bistable behavior of the system in dielectric slab can be controlled via amplitude or relative phase of applied fields. This optical system may provide some new possibilities for test the switching process.     

Optical bistability via amplitude and phase control of a microwave field

We investigate the steady-state optical bistability behavior in a three-level Λ-type atomic system closed by a microwave field under the condition that the applied fields are in resonance with corresponding atomic transitions. It is shown that the bistable hysteresis cycles can be controlled by both the amplitude and the phase of the microwave field.     

光学简并三波混频中的量子非破坏测量

运用半经典量子理论方法建立了光学简并三波混频在两输入场均不为零的情况下的理论模型 ,讨论了在两输入场均不为零时系统的动力学行为以及相应的量子非破坏测量 (QND)特性。研究结果表明 ,该系统的最佳量子非破坏测量工作点与以往的情况不同 ,不是出现在非线性共振点处而是在双稳转变点     

Optical bistability and differential amplification in a tapered fiber coupler — microsphere resonator with nonlinear medium

We propose and study a coupling system composed of the tapered fiber and the microsphere with nonlinear medium. The optical bistability and differential amplification caused by optical Kerr effect is demonstrated using a geometrical method. We show that their operation characteristics can be controlled by parameters: linear phase detuning, attenuation coefficient and real amplitude coupling coefficient.     

A finite element scheme to study the nonlinear optical response of a finite grating without and with defect

We present a simple numerical scheme based on the finite element method (FEM) using transparent-influx boundary conditions to study the nonlinear optical response of a finite one-dimensional grating with Kerr medium. Restricting first to the linear case, we improve the standard FEM to get a fourth order accurate scheme maintaining a symmetric-tridiagonal structure of the finite element matrix. For the full nonlinear equation, we implement the improved FEM for the linear part and a standard FEM for the nonlinear part. The resulting nonlinear system of equations is solved using a weighted-averaged fixed-point iterative method combined with a continuation method. To illustrate the method, we study a periodic structure without and with defect and show that the method has no problem with large nonlinear effect. The method is also found to be able to show the optical bistability behavior of the ideal and the defect structure as a function of either the frequency or the intensity of the input light. The bistability of the ideal periodic structure can be obtained by tuning the frequency to a value close to the bottom or top linear band-edge while that of the defect structure can be produced using a frequency near the defect mode or near the bottom of the linear band-edge. The threshold value can be reduced by increasing the number of layer periods. We found that the threshold needed for the defect structure is much lower then that for a strictly periodic structure of the same length.