Eliminating spiral waves and spatiotemporal chaos using feedback signal

Spiral waves and spatiotemporal chaos are sometimes harmful and should be controlled. In this letter we present a feedback scheme to eliminate them. We first collect feedback signals at a certain time t₀. Then wait for the system at the excitable position to enter the recovering state. When the time comes, the feedback signals are added. This scheme has two advantages. Firstly, the tip can be eliminated together with the body of spiral wave. Secondly, the injected feedback signals can be very weak and the duration can be very short so that the original system is nearly not to be affected, which is important for practical applications.     

Nodal domains statistics: a criterion for quantum chaos

We consider the distribution of the (properly normalized) numbers of nodal domains of wave functions in 2D quantum billiards. We show that these distributions distinguish clearly between systems with integrable (separable) or chaotic underlying classical dynamics, and for each case the limiting distribution is universal (system independent). Thus, a new criterion for quantum chaos is provided by the statistics of the wave functions, which complements the well-established criterion based on spectral statistics.     

A family of driving forces to suppress chaos in jerk equations: Laplace domain design

A family of driving forces is discussed in the context of chaos suppression in the Laplace domain. This idea can be attained by increasing the order of the polynomial in the expressions of the driving force to account for the robustness and/or the performance of the closed loop. The motivation arises from the fact that chaotic systems can be controlled by increasing the order of the Laplace controllers even to track arbitrary orbits. However, a larger order in the driving forces can induce an undesirable frequency response, and the control efforts can result in either peaking or large energy accumulation. We overcame these problems by showing that considering the frequency response (interpreted by norms), the closed-loop execution can be improved by designing the feedback suppressor in the Laplace domain. In this manner, the stabilization of the chaotic behavior in jerk-like systems is achieved experimentally. Jerk systems are particularly sensitive to control performance (and robustness issues) because the acceleration time-derivative is involved in their models. Thus, jerky systems are especially helped by a robust control design.     

Chaos synchronization in RCL-shunted Josephson junctions via a common chaos driving

We study chaos synchronization in two resistive-capacitive-inductive-shunted (RCL-shunted) Josephson junctions (RCLSJJs) by using a common chaos driving. The numerical simulations confirm that the synchronization of two RCLSJJs can be achieved with a suitable driving intensity when the maximum condition Lyapunov exponent (MCLE) is negative.     

用多凹槽滤波器控制混沌系统

提出了一种施加多个凹槽滤波器反馈控制混沌系统的方法,使混沌运动转化为规则的运动.多凹槽滤波器控制是一种具有固定参数的线性反馈控制方法,它不影响原系统的参数,截断了系统从倍周期分叉通向混沌的道路.同时,用Melnikov方法进行理论分析,给出了合适的反馈控制器的参数.将多凹槽滤波器应用于典型的混沌系统,其仿真结果表明了该控制方法的有效性与可行性 关键词： 混沌 多凹槽滤波器 Melnikov方法     

Probing quantum dissipative chaos using purity

In this Letter, the purity of quantum states is applied to probe chaotic dissipative dynamics. To achieve this goal, a comparative analysis of regular and chaotic regimes of nonlinear dissipative oscillator (NDO) are performed on the base of excitation number and the purity of oscillatory states. While the chaotic regime is identified in our semiclassical approach by means of strange attractors in Poincaré section and with the Lyapunov exponent, the state in the quantum regime is treated via the Wigner function. Specifically, interesting quantum purity effects that accompany the chaotic dynamics are elucidated in this Letter for NDO system driven by either: (i) a time-modulated field, or (ii) a sequence of pulses with Gaussian time-dependent envelopes.     

Channel coding in communications using chaos

We introduce a novel chaotic channel code with error-correcting capabilities. This channel code takes advantage of the natural redundancy contained in the perturbations applied to a chaotic system, in order to encode a desired message in the symbolic dynamics of the chaotic waveform.     

New estimate on the domains of attraction of equilibrium points in continuous Hopfield neural networks

This Letter addresses the qualitative properties of equilibrium points in continuous Hopfield neural networks. We derive a sufficient condition for an equilibrium point to be locally exponentially stable. We also present an estimate on the domains of attraction of locally exponentially stable equilibrium points. Our condition and estimate are formulated in terms of the network parameters, the neurons' activation functions and the associated equilibrium point. Hence, they are easily checkable. In addition, these results neither depend on the monotonicity of the activation functions nor on coupling conditions between the neurons. Consequently, our results are of practical importance in the evaluation of performance of Hopfield associative memory networks.     

混沌的模糊神经网络逆系统控制

提出用Sugeno型的模糊推理神经网络建立混沌系统的逆系统模型,并采用逆系统方法进行混沌的控制.这种方法的特点是可以不必建立混沌系统的解析模型,通过模糊神经网络学习混沌系统的运动规律,通过学习获得的规律对混沌进行有效的控制,并且该控制方法可以控制混沌系统以一定精度跟踪连续变化的给定信号.理论分析及针对虫口模型和Henon模型仿真研究证明了该方法的有效性 关键词： 混沌 模糊神经网络 逆系统控制     

Robust chaos synchronization of noise-perturbed chaotic systems with multiple time-delays

The aim of this paper is to propose an output coupling and feedback scheme, which is not only to guarantee the asymptotic synchronization between the master and the slave chaotic systems with multiple time-delays but also to attenuate the effects of noise perturbation on the overall error system to a prescribed level in terms of the performance index H_∞-norm. The output coupling and feedback gain is derived on the basis of the Lyapunov theory and the linear matrix inequality (LMI) technique. Some numerical examples are given to demonstrate the effectiveness of the main results.     

通过抑制波头旋转消除心脏中的螺旋波和时空混沌

本文采用Luo-Rudy相I模型研究如何通过调控心肌细胞钠电流变化来控制心脏中的螺旋波和时空混沌,提出了这样的钠电流调控方案:当细胞将被激发时启动钠电流调节,若由模型方程得到的钠电流的绝对值小于钠电流控制阈值的绝对值,就让钠电流等于钠电流控制阈值,其他情况下则限制钠电流的绝对值不能高于一个给定的最大值;当膜电位上升超过-5 mV时,让钠电流自然演化.这种调节钠电流的方式保证了所有细胞几乎具有相同的钠电流幅值,从而使所有细胞具有相同的激发性,数值模拟结果表明,只要钠电流控制阈值达到一定临界值,就可以有效抑制螺旋波波头的旋转,导致螺旋波运动出系统边界而消失,以及时空混沌演化为螺旋波后消失,如果钠电流控制阈值足够大,螺旋波和时空混沌还可通过传导障碍而消失.这些结果能够为抗心律失常治疗提供新的思路.     

Transient chaos measurements using finite-time Lyapunov exponents

The notion of finite-time Lyapunov exponent averaged over initial conditions is used for characterizing transient chaos observed in one-dimensional maps. A model of its dependence on time is verified by comparing theoretically predicted values with those obtained numerically. Finally, the same model is used for estimating duration of transient chaos (rambling time) for some maps from the logistic family.     

半周期延迟-非线性反馈控制混沌

提出了基于稳定性准则的半周期延迟-非线性反馈控制混沌的方法，即SC(stability criterion)半周期延迟非线性反馈控制法.通过对混沌系统的适当分离，得到一个特殊的非线性函数，并利用混沌输出信号与其半周期延迟信号的非线性函数之和，构造了连续反馈输入干扰.该方法继承了延迟反馈控制方法及稳定性准则控制方法的优点，实现了有效的自控制过程；并克服了延迟反馈方法的限制，能将嵌入混沌吸引子中的自对称直接不稳周期轨稳定.控制过程可随时开始，具有简便、灵活性.数值模拟结果显示了SC半周期延迟-非线性反馈方法控制的有效性. 关键词： 稳定性准则 混沌控制 半周期延迟 非线性反馈     

Reducing or enhancing chaos using periodic orbits

A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local bifurcations). Depending on the values of the residues, reflecting their linear stability properties, a set of invariant tori is destroyed or created in the neighborhood of the chosen periodic orbits. An application on a paradigmatic system, a forced pendulum, illustrates the method.     

Synchronization of spatiotemporal chemical chaos using random signals

We report the synchronization of two uncoupled spatially extended chemical systems by superimposing identical external random signals to both of them. In one spatial dimension, under appropriate parameter conditions the model systems exhibits a transition to turbulence via backfiring of pulses. Implementing the non-vanishing random signal control to the underlying partial differential equations, synchronization is achieved not only for identical systems, but also for systems operating under unequal parameter values exhibiting a different dynamical behavior (generalized synchronization). Finally, synchronization is also achieved under the influence of a random signal superimposed globally, thus making it relevant to experimental situations.     

Shapes of lipid monolayer domains: Solutions using elliptic functions

Solid lipid monolayer domains surrounded by a fluid phase at an air-water interface exhibit complex shapes. These intriguing shapes can be understood in terms of a competition between line tension and long-range dipole-dipole interaction. The dipolar energy has recently been relevant to a negative line tension and a positive curvature energy at the boundary, and a corresponding shape equation was derived by the variation of the approximated domain energy (Phys. Rev. Lett. 93, 206101 (2004)). Here we further incorporate surface pressure into the shape equation and show that the equation can be analytically solved: the curvature of the domain boundary is exactly obtained as an elliptic function of arc-length. We find that a circular domain can grow into bean-and peach-like domains with pressure, i.e., dipping and cuspidal transitions of circle by compression. The comparison with the experimental observation shows nice agreement.     

研究多中心奇异吸引子混沌相位的新方法

对一般混沌轨迹的相位定义进行了研究,考虑到大量的混沌运动投影到相平面后不是只有一个转动中心的正规转动,给出了两种计算瞬时相位的简单方法.一种方法称之为直接分解方法,它是基于分解的思想.另一种是切线方法,它需要计算轨迹在切空间中的角度.通过对一些算例结果的比较,可以看出这两种方法的优越性.综合而言,切线方法是对任意混沌振动适用的,因此可以被广泛应用于混沌相位同步的研究中 关键词： 混沌同步 相位同步 正规转动     

Gyrator transform-based optical image encryption,using chaos

We propose a new method for image encryption, using gyrator transform and chaos theory. Random phase masks are generated using chaos functions and are called as chaotic random phase masks. In the proposed technique, the image is encrypted using gyrator transform and two chaotic random phase masks. Three types of chaos functions have been used to generate the chaotic random phase masks. These chaos functions are the logistic map, the tent map and the Kaplan-Yorke map. The computer simulations are presented to verify the validity of the proposed technique. The mean square errors have been calculated. The robustness of the proposed technique to blind decryption in terms of rotation angle and the seed values of the chaotic random phase mask have been evaluated. The optical implementation of the encryption and the decryption technique has been proposed.