Controlling Chaos in Hénon Map by the Constant Feedback Method

We demonstrate the constant feedback and the modified constant feedback method to the Hénon map. Using the convergence of the chaotic orbit in finite time, we can control the system from chaos to the stable fixed point, and even to the stable period-2 orbit or higher periodic orbit by the action of a proper feedback strength and pulse interval. We also find that the multi-steady solutions appear with the same control strength and different initial conditions. The aim of this control method is explicit and the feedback strength is easy to determine. The method is robust under the presence of weak external noise.     

A control method applied to mixed traffic flow for the coupled-map car-following model

In light of previous work [Phys. Rev. E 60 4000 （1999）], a modified coupled-map car-following model is proposed by considering the headways of two successive vehicles in front of a considered vehicle described by the optimal velocity function. The non-jam conditions are given on the basis of control theory. Through simulation, we find that our model can exhibit a better effect as p = 0.65, which is a parameter in the optimal velocity function. The control scheme, which was proposed by Zhao and Gao, is introduced into the modified model and the feedback gain range is determined. In addition, a modified control method is applied to a mixed traffic system that consists of two types of vehicle. The range of gains is also obtained by theoretical analysis. Comparisons between our method and that of Zhao and Gao are carried out, and the corresponding numerical simulation results demonstrate that the temporal behavior of traffic flow obtained using our method is better than that proposed by Zhao and Gao in mixed traffic systems.     

Chaos Control and Anti-control via a Fuzzy Neural Network Inverse System Method

We propose a new method for chaos control and anti-control,which is referred to as the fuzzy-neural network inverse system method (FNNIS).The Sugeno-type fuzzy-neural network (FNN) is employed to learn the kinetics of the system to be controlled.Then the FNN model is used with the inverse system method to make the system to be controlled to track the reference input.If the system to be controlled is chaotic and the reference input is non-chaotic,chaos control can be implemented via the FNNIS method.If the system to be controlled is nonchaotic and the reference imput is chaotic,chaos anti-control can be implemented.Theorems about the effect of the FNN model error upon control are established.The simulation results show that this method is feasible and effective for chaos control and anti-control.     

Controlling Chaos in Hénon Map by the Constant Feedback Method

We demonstrate the constant feedback and the modified constant feedback method to the Hénon map. Using the convergence of the chaotic orbit in finite time, we can control the system from chaos to the stable fixed point, and even to the stable period-2 orbit or higher periodic orbit by the action of a proper feedback strength and pulse interval. We also find that the multi-steady solutions appear with the same control strength and different initial conditions. The aim of this control method is explicit and the feedback strength is easy to determine. The method is robust under the presence of weak external noise.     

Control of the patterns by using time-delayed feedback near the codimension-three Turing–Hopf–Wave bifurcations

Control of the spatiotemporal patterns near the codimension-three Turing–Hopf–Wave bifurcations is studied by using time-delayed feedback in a three-variable Brusselator model. Linear stability analysis of the system shows that the competition among the Turing-, Hopf- and Wave-modes, the wavenumber, and the oscillation frequency of patterns can be controlled by changing the feedback parameters. The role of the feedback intensity Pu played on controlling the pattern competition is equivalent to that of Pw, but opposite to that of Pv. The role of the feedback intensity Pu played on controlling the wavenumber and oscillation frequency of patterns is equivalent to that of Pv, but opposite to that of Pw. When the intensities of feedback are applied equally, changing the delayed time could not alter the competition among these modes, however, it can control the oscillation frequency of patterns. The analytical results are verified by two-dimensional （2D） numerical simulations.     

Control of Beam Halo-Chaos for an Intense Charged-Particle Beam Propagating Through Double Periodic Focusing Field by Soliton

We study an intense beam propagating through the double periodic focusing channel by the particle-core model, and obtain the beam envelope equation. According to the Poincare-Lyapunov theorem, we analyze the stability of beam envelope equation and find the beam halo. The soliton control method for controlling the beam halo-chaos is put forward based on mechanism of halo formation and strategy of controlling beam halo-chaos, and we also prove the validity of the control method, and furthermore, the feasible experimental project is given. We perform multiparticle simulation to control the halo by using the soliton controller. It is shown that our control method is effective. We also find the radial ion density changes when the ion beam is in the channel, not only the halo-chaos and its regeneration can be eliminated by using the nonlinear control method, but also the density uniformity can be found at beam＇s centre as long as an appropriate control method is chosen.     

Feedback control of two-headed Brownian motors in flashing ratchet potential

We presented a detailed investigation on the movement of two-headed Brownian motors in an asymmetric potential under a feedback control.By numerical simulations the direct current is obtained.The current is periodic in the initial length of spring.There is an optimal value of the spring constant.And the dependence of the current on the opposing force is reversed.Then we found that when the change of the temperature and the opposing force have optimal values,the Brownian motors can also obtain the optimal efficiency.     

Characterizing a liquid crystal spatial light modulator at oblique incidence angles using the self-interference method

The phase modulation characteristics of a reflective liquid crystal(LC) spatial light modulator(SLM) under oblique incidence are studied by using our proposed self-interference method. The experimental setup of the method is very simple and has good robustness to mechanical vibrations. By changing the gray value of the combined grayscale loaded on the LC-SLM, different sheared fringe patterns, generated by the interference between the constant phase-modulated beam and the +1-order diffracted beam of the blazed grating, can be obtained. The amount of phase modulation of the LC-SLM is obtained by subtracting the phase of the two side lobes in the frequency domain. By turning the turntable where the SLM is mounted, the phase modulation characteristics at different incident angles can be measured. The experimental results show that the phase modulation curves do not change significantly with the small angle. When the angle is large(i.e. larger than 10°), the phase modulation curves become different, especially for the high gray levels. With the increase of the incident angle, the phase modulation depth is reduced. The results indicate that the incident angle plays an important role in the performance of the phase modulation of an LC-SLM.     

Stability of GOY Model Under Modulation of Periodic External Force

There is a phase transition between quasi-periodic state and intermittent chaos in GOY model with a critical value δ0. When we add a modulated periodic externa/force to the system, the phase transition can also be found with a critical value δe. Due to coupling between the force and the intrinsic fluctuation of the velocity on shells in GOY model, the stability of the system has been changed, which results in the variation of the critical value. For proper intensity and period of the force, δe is unequal to δ0. The critical value is a nonlinear function of amplitude of the force, and the fluctuation of the velocity can resonate with the external force for certain period Te.     

The antiferromagnetic Potts model in two dimensions: Berker-Kadanoff phase, antiferromagnetic transition, and the role of Beraha numbers

Using methods of integrable systems and conformal field theory, we study the Q-state Potts model on the square lattice with e^K real. We discover a surprisingly rich phase diagram that involves, besides the usual ferromagnetic critical line, an antiferromagnetic critical line and a Berker-Kadanoff phase (i.e., a massless low-temperature phase with coupling-independent exponents) that has singularities at the Baraha numbers (including Q integer) Q = 4cos²π/n. Critical properties are derived; we show in particular that the Q = 4cos²π/δ antiferromagnetic critical Potts model is in the “Z_δ−2” universality class with c = 2−6/δ. Extensions to other lattices are considered. We discuss the consequences of our results on the coloring problem and the Beraha conjecture. Three appendices deal with the geometrical interpretation of the Temperley-Lieb algebra and U_qsl(2) symmetry in the Potts and associated loops model, and with the vertex-Potts model correspondence in systems with free boundary conditions.     

Numerical and experimental exploration of phase control of chaos

A well-known method to suppress chaos in a periodically forced chaotic system is to add a harmonic perturbation. The phase control of chaos scheme uses the phase difference between a small added harmonic perturbation and the main driving to suppress chaos, leading the system to different periodic orbits. Using the Duffing oscillator as a paradigm, we present here an in-depth study of this technique. A thorough numerical exploration has been made focused in the important role played by the phase, from which new interesting patterns in parameter space have appeared. On the other hand, our novel experimental implementation of phase control in an electronic circuit confirms both the well-known features of this method and the new ones detected numerically. All this may help in future implementations of phase control of chaos, which is globally confirmed here to be robust and easy to implement experimentally.     

参数共振微扰法在Boost变换器混沌控制中的实现及其优化

参数共振微扰法是一种简单的非反馈混沌控制方法，它十分适合非自治系统的混沌控制.研究了这种方法在电流模式控制Boost变换器混沌控制中的应用，并通过对扰动相位进行优化 ，达到最优的混沌控制结果.同时对参数共振微扰法及其优化方法在Boost变换器混沌控制中的作用进行了理论分析，推导并计算了各种电路参数变化对有效的混沌控制所需的扰动的影响. 关键词： Boost变换器 混沌 混沌控制 参数共振微扰法     

Modeling the dynamics of firms' technological impact

Recent studies in complexity science have uncovered temporal regularities in the dynamics of impact along scientific and other creative careers, but they did not extend the obtained insights to firms. In this paper, we show that firms' technological impact patterns cannot be captured by the state-of-the-art dynamical models for the evolution of scientists' research impact, such as the Q model. Therefore, we propose a time-varying returns model which integrates the empirically-observed relation between patent order and technological impact into the Q model. The proposed model can reproduce the timing pattern of firms' highest-impact patents accurately. Our results shed light on modeling the differences behind the impact dynamics of researchers and firms.     

Switchable vortex beam polarization state terahertz multi-layer metasurface

We propose a switchable vortex beam polarization state terahertz multi-layer metasurface, which consists of three-layer elliptical metal crosses, four-layer dielectrics, and two-layer hollow metal circles, which are alternately superimposed. Under the normal incidence of left-handed circularly polarized (LCP) wave and the right-handed circularly polarized (RCP) waves, the proposed structure realizes three independent control functions, i.e., focused and vortex beam, vortex beam with different topological charges, and polarization states switching, and azimuth switching of two vortex beams with different polarization states. The results show that the proposed metasurface provides a new idea for investigating the multifunctional terahertz wave modulation devices.     

Chaotic phase oscillation of a proton beam in a synchrotron

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.     

Electromagnetically induced transparency in novel dual-band metamaterial excited by toroidal dipolar response

We demonstrated a novel metamaterial with dual-band electromagnetically induced transparency(EIT)via simulation,experiment and numerical analysis,with resonance frequencies of the trans-parency peaks of 7.60 and 10.27 GHz.The E-εmetamaterial unit cells were composed of E-shaped and e-shaped patterns.By analyzing the surface current distribution and the magnetic field,we qualitatively verified the toroidal dipole response in the E-εmetamaterial at 10.27 GHz.Meanwhile,by calculating the multipole's radiated power,we found that the two transparency peaks were due to the excitation of the electric and toroidal dipole responses.By changing the incident angle from 0°to 60°,we observed changes in transmission spectra,and the quality factors(Q-factors)of the two transparency peaks increased.In addition,the proposed E-εmetamaterial can be designed to act as a refractive index sensor or other electronic equipment for the control of electromagnetic waves.     

低场核磁共振仪器振铃抑制新方法及其电路实现

加快天线残余能量释放以减弱天线振铃信号有利于缩短低场核磁共振仪器的回波间隔（TE）,从而提高快弛豫组分的测量分辨率和信噪比（SNR）．而天线Q值对能量的发射效率和泄放速度起着相反的作用．为此,我们首先设计了一种新型Q转换电路,在保证发射效率的同时,可以大大缩短能量泄放时间．在此基础上,应用了一种优化的脉冲序列以弥补传统相位交替对脉冲序列（PAPs）不能消除90°脉冲振铃的缺陷,通过相位循环的方法进一步提高了信噪比．最后,在2 MHz岩心分析仪上测试了新型Q转换电路,当天线Q值降为发射期间的约1/5时,天线恢复时间由280.0 μs降为18.2 μs;而且,使用新型Q转换电路和优化的脉冲序列后,TE=60 μs时,可以有效获得快弛豫组分的T₂信号．     

Noncommutative supergeometry, duality and deformations

Following Lett. Math. Phys. 50 (1999) 309, we introduce a notion of Q-algebra that can be considered as a generalization of the notion of Q-manifold (a supermanifold equipped with an odd vector field obeying {Q,Q}=0). We develop the theory of connections on modules over Q-algebras and prove a general duality theorem for gauge theories on such modules. This theorem containing as a simplest case SO(d,d,Z)-duality of gauge theories on noncommutative tori can be applied also in more complicated situations. We show that Q-algebras appear naturally in Fedosov construction of formal deformation of commutative algebras of functions and that similar Q-algebras can be constructed also in the case when the deformation parameter is not formal.     

Quantum algorithm for neighborhood preserving embedding

Neighborhood preserving embedding (NPE) is an important linear dimensionality reduction technique that aims at preserving the local manifold structure. NPE contains three steps, i.e., finding the nearest neighbors of each data point, constructing the weight matrix, and obtaining the transformation matrix. Liang et al. proposed a variational quantum algorithm (VQA) for NPE [Phys. Rev. A 101 032323 (2020)]. The algorithm consists of three quantum sub-algorithms, corresponding to the three steps of NPE, and was expected to have an exponential speedup on the dimensionality n. However, the algorithm has two disadvantages: (i) It is not known how to efficiently obtain the input of the third sub-algorithm from the output of the second one. (ii) Its complexity cannot be rigorously analyzed because the third sub-algorithm in it is a VQA. In this paper, we propose a complete quantum algorithm for NPE, in which we redesign the three sub-algorithms and give a rigorous complexity analysis. It is shown that our algorithm can achieve a polynomial speedup on the number of data points m and an exponential speedup on the dimensionality n under certain conditions over the classical NPE algorithm, and achieve a significant speedup compared to Liang et al.'s algorithm even without considering the complexity of the VQA.