Dynamics of Meandering Spiral Waves Driven by Two-Point Feedback

We numerically study the dynamics of meandering spiral waves in theexcitable system subjected to a feedback signal coming from two measuring points located on a straight line together with the initial spiral core. The core location and size radius of the final attractors are computed, and they change with the position of the moving measuring point in a unique way. By the Fourier Spectral analysis, we find the frequency-locked behaviors different from the
driving scheme of the external periodic force. It is also found that the meandering spiral wave can be eliminated when the moving measuring point approaches closely the boundary and its feedback gain is large enough. This offers an effective and convenient method for eliminating meandering spiral waves.     

环域反馈下复Ginzburg-Landau系统的螺旋波动力学行为

针对自激振荡系统的复金兹伯格-朗道(Complex Ginzbury-Landau, 简称CGL)方程, 研究圆形环域与方形环域两种反馈控制下的螺旋波动力学。结果表明: 圆形环域反馈控制下, 螺旋波波头通常经过一段过渡漂移后进入圆形吸引子, 圆形吸引子的半径以及反馈刚启动时波头的漂移方向随环域参数呈周期性变化, 过渡漂移阶段波头轨道的平缓程度与复反馈信号模的时间函数中钟形部分的陡度有关, 且反馈增益的正负与大小也会影响受控螺旋波的动力学行为。方形环域反馈控制下的螺旋波波头的吸引子更为丰富, 主要包括方形吸引子、小的极限环吸引子、菱形吸引子以及点吸引子, 点吸引子通常位于方形环域的两条对角线上, 且波头运动随环域控制参数呈现规律性变换。     

Dynamics of Spiral Waves Induced by Periodic Mechanical Deformation with Phase Difference

The dynamics of spiral waves under the influences of periodic mechanical deformation are studied. Here, the mechanical deformation propagating along the medium with phase differences are considered. It is found that weak mechanical deformation may lead to resonant drift of spiral waves. The drift direction and velocity can be changed by the wave length of the deformation. Strong mechanical deformation may result in breakup of spiral waves. The characteristics of breakup are discussed. The critical amplitudes are determined by two factors, i.e. the wave length and frequency of the periodic mechanical deformation. When the wave length of mechanical deformation is comparable to the spiral wave, simulation shows that the critical amplitude is substantially increased. As the frequency of the mechanical deformation is around 1.5 times of the spiral wave, the critical amplitudes are minimal.     

Dynamics of Vortex-Wave under a Travelling-Wave Modulation

The mechanism of destabilization is studied for the rotating vortices （scroll waves and spiral waves） in excitable media induced by a parameter modulation in the form of a travelling-wave. It is found that a rigid rotating spiral in the two-dimensional （2D） system undergoes a synchronized drift along a straight line, and a 3D scroll ring with its filament closed into a circle can be reoriented only if the direction of wave number of a travelling-wave perturbation is parallel to the ring plane. Then, in order to describe the behaviour of the synchronized drift of spiral wave and the reorientation of scroll ring, the approximate formulas are given to exhibit qualitative agreements with the observed results.     

Nucleation, drift, and decay of phase bubbles in period-2 oscillatory wave trains in a reaction-diffusion system

This is a report on experimental observations of phase bubbles, simply closed boundaries between domains oscillating 2pi out of phase, associated with period-2 oscillatory traveling waves in a Belousov-Zhabotinsky reaction-diffusion system. The bubbles nucleate spontaneously through a fast localized phase slip, drift radially away from a neighboring spiral wave core in an oscillatory fashion, and gradually shrink to disappear. Their oscillatory drift along the radial direction is a consequence of "period adaptation," while their lateral shrinkage is an attribute of local curvature. Similar dynamic structures can be reproduced in a simple, three-species reaction-diffusion model that supports period-2 oscillatory wave trains.     

非连续反馈控制激发介质中的螺旋波

采用非连续反馈方法来控制Fitz-Hugh-Nagumo方程描述的激发介质中的螺旋波. 在控制过程中,对于系统各个格点快变量的幅值进行观测并和设定的阈值进行比较,当采样格点的快变量的值大于这个阈值时,则对系统进行直接小幅度的负反馈. 研究发现：在对系统所有格点快变量幅值观测时选择比较小的阈值则更容易将系统的螺旋波消除掉并使系统达到稳定均匀态. 在比较大的阈值下,系统的螺旋波则变得稀疏,也可以导致螺旋波的破裂. 在任意选择单个格点的快变量观测下,比较小的反馈强度仍然可以消除螺旋波,系统也达到稳定均匀态. 当 关键词： 螺旋波 Fitz-Hugh-Nagumo方程 反馈控制     

Spiral wave drift induced by stimulating wave trains

We investigate the drift of a spiral wave core in a homogeneous excitable medium under the influence of a periodic stimulation by wave trains close to the core. Two important results were found. First, as opposed to existing theories of spiral wave drift, we observe drift induced by wave trains with periods larger than the period of the freely rotating spiral wave. Second, when investigating the drift of meandering spirals we found that the property of meandering of spirals is not robust against periodic stimulations. Simple phenomenological arguments are provided to explain these observations. (c) 2001 American Institute of Physics.     

Tunneling chemical waves

Summary  The tunneling of chemical waves through the gaps of different geometrical shapes was studied using a new experimental model based on the polysulphone membranes with the fixed catalyst. Period doubling of the wave train, formation of the wave breaks on the split in polysulphone membrane, drift of the spiral wave along the widening split were observed. The effects were confirmed and studied in details using computer simulation.     

局域反馈抑制心脏中的螺旋波和时空混沌

采用LuoRud91模型研究了螺旋波和时空混沌的抑制,提出用局域反馈控制方法抑制螺旋波和时空混沌,采用静止和运动控制器两种控制策略.结果表明:适当选择控制参数,静止控制器的局域反馈方法能很好抑制螺旋波,但不能有效抑制时空混沌;采用运动控制器的局域反馈方法能有效抑制螺旋波和时空混沌,抑制速度与控制器移动的速度有关,在选择适当的控制参数下,螺旋波和时空混沌能在很短的时间内被抑制.     

Electrical alternans and spiral wave breakup in cardiac tissue

This paper reports the results of a theoretical investigation of spiral wave breakup in model equations of action potential propagation in cardiac tissue. A general formulation of these equations is described in which arbitrary experimentally determined restitution and dispersion curves can in principle be fitted. Spiral wave behavior is studied in two-dimension as a function of a parameter Re which controls the steepness of the restitution curve at short diastolic intervals. Spiral breakup is found to occur when the minimum period T(min), below which a periodically stimulated tissue exhibits alternans in action potential duration, exceeds by a finite amount the spiral rotation period T(S). At this point, oscillations in action potential duration are of sufficiently large amplitude to cause a spontaneous conduction block to form along the wavefront. The latter occurs closer to the initiation point of reentry (spiral tip) with increasing steepness and, hence, in smaller tissue sizes. Spiral breakup leads to a spatially disorganized wave activity which is always transient, except for tissues larger than some minimum size and within a very narrow range of Re which increases with dispersion.     

间接延迟耦合可激发介质中螺旋波的演化

采用Bär 模型研究了通过被动介质间接延迟耦合的两层可激发介质中螺旋波的相互作用. 数值模拟结果表明: 延迟耦合可以促进两个螺旋波的同步, 也可导致从螺旋波到集体振荡、各种靶波、时空混沌态或静息态的转变; 在这个耦合系统中还观察到周期 2和周期3螺旋波以及螺旋波漫游和漂移现象; 对产生这些现象的物理机制做了讨论. 关键词： 螺旋波 被动介质 时间延迟耦合 同步     

Optical target and spiral patterns in a single-mirror feedback scheme

Spatio-temporal structures with a regular time dependence are observed in a nonlinear optical system consisting of a sodium-vapour cell and a single feedback mirror. Target and spiral patterns appear spontaneously in the intensity of the transmitted light field as a result of a self-organisation process. In contrast to the results obtained in most other pattern-forming systems, the radial motion of the waves is directed towards the centre. The emergence of oscillatory structures is traced back to a Hopf bifurcation at a finite wave number. The preference for a radial drift motion is due to a nonlinear guiding effect which results from phase gradients created by the inhomogeneous pump profile. The direction of the drift can be reversed by externally applied phase gradients. The system is a striking example of a case in which the radial variation of the pump profile has a decisive influence on pattern formation. Received: 31 July 2002 / Revised version: 30 October 2002 / Published online: 26 February 2003 RID="*" ID="*"Corresponding author. Fax: +49-251/83-33513, E-mail: huneus@uni-muenster.de     

具有早期后除极化现象的可激发系统中螺旋波破碎方式研究

在Greenberg-Hasting元胞自动机模型中引入了正常元胞和老化元胞,并规定只有老化元胞存在早期后除极化现象且早期后除极化可以激发其他元胞.在正常元胞和老化元胞均匀分布的情况下,研究了早期后除极化对螺旋波演化行为的影响,重点探讨了早期后除极化导致的螺旋波破碎方式.数值模拟结果表明:早期后除极化在比率约为26.4%的少数情况下不对螺旋波产生影响,在其他情况下则会对螺旋波产生各种影响,包括使螺旋波漫游、漂移、波臂发生形变以及导致螺旋波破碎和消失等.观察到早期后除极化通过传导障碍消失和通过转变为反靶波消失,早期后除极化导致螺旋波破碎有8种方式,包括非对称破缺导致的破碎、对称破缺导致的破碎、同时激发双波导致的破碎、非对称激发导致的破碎、整体传导障碍导致的破碎、整体快速破碎等.分析发现这些螺旋波破碎现象都与早期后除极化产生回火波有关,得到螺旋波破碎的总比率通常约为13.8%,但是在适当选取老化元胞密度和早期后除极化的激发下,螺旋波破碎比率可达到32.4%,这些结果与心律失常致死的统计结果基本一致,本文对产生这些现象的物理机理做了简要分析.     

Large-deviation properties of resilience of transportation networks

In this study, we consider a propagating wave segment in two dimensions. A reaction diffusion system with global feedback is proposed, and spiral waves and propagating wave segments are shown. Propagating wave segments with large arc lengths can exist due to the absence of strong lateral inhibition. In order to study the properties of propagating wave segments, we propose a kinematic model with global feedback. When the elongating and shortening effects on the curve are balanced, stable propagating wave segments exist. For other cases, the initial wave segment evolves into a spiral wave or expanding wave or shrinking wave. The conditions for the propagating wave segment and the dependences of the solutions on the various relevant parameters are discussed.     

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.     

Segmented Spiral Waves and Anti-phase Synchronization in a Model System with Two Identical Time-Delayed Coupled Layers

In this paper, we consider a model system with two identical time-delayed coupled layers. Synchronization and anti-phase synchronization are exhibited in the reactive system without diffusion term. New segmented spiral waves, which are constituted by many thin trips, are found in each layer of two identical time-delayed coupled layers, and are different from the segmented spiral waves in a water-in-oil aerosol sodium bis（2-ethylhexyl） sulfosuccinate （AOT） microemulsion （ME） （BZ-AOT system）, which consists of many small segments. ＂Anti-phase spiral wave synchronization＂ can be realized between the first layer and the second one. For different excitable parameters, we also give the minimum values of the coupling strength to generate segmented spiral waves and the tip orbits of spiral waves in the whole bilayer.     

矩形弹子球中的量子波包分析(英文)

利用波包分析量子力学体系的动力学行为在研究经典和量子的对应关系方面越来越成为一个非常重要的方法.利用高斯波包分析方法,我们计算了矩形弹子球体系的自关联函数,自关联函数的峰和经典周期轨道的周期符合的很好,这表明经典周期轨道的周期可以通过含时的量子波包方法产生.我们还讨论了矩形弹子球的波包回归和波包的部分回归,计算结果表明在每一个回归时间,波包出现精确的回归.对于动量为零的波包,初始位置在弹子球内部的特殊对称点处,出现一些时间比较短的附加的回归.     

Acoustic propagation from a spiral wave front source in an ocean environment

A spiral wave front source generates a pressure field that has a phase that depends linearly on the azimuthal angle at which it is measured. This differs from a point source that has a phase that is constant with direction. The spiral wave front source has been developed for use in navigation; however, very little work has been done to model this source in an ocean environment. To this end, the spiral wave front analogue of the acoustic point source is developed and is shown to be related to the point source through a simple transformation. This makes it possible to transform the point source solution in a particular ocean environment into the solution for a spiral source in the same environment. Applications of this transformation are presented for a spiral source near the ocean surface and seafloor as well as for the more general case of propagation in a horizontally stratified waveguide.     

Theoretical and experimental study of discrete behavior of Shilnikov chaos in a CO 2 laser

The discrete distribution of homoclinic orbits has been investigated numerically and experimentally in a CO₂ laser with feedback. The narrow chaotic ranges appear consequently when a laser parameter (bias voltage or feedback gain) changes exponentially. Up to six consecutive chaotic windows have been observed in the numerical simulation as well as in the experiments. Every subsequent increase in the number of loops in the upward spiral around the saddle focus is accompanied by the appearance of the corresponding chaotic window. The discrete character of homoclinic chaos is also demonstrated through bifurcation diagrams, eigenvalues of the fixed point, return maps, and return times of the return maps. Received 28 September 2000 and 27 October 2000     

Drift of Spiral Waves in Complex Ginzburg-Landau Equation

The spontaneous drift of the spiral wave in a finite domain in the complex Ginzburg-Landau equation is investigated numerically. By using the interactions between the spiral wave and its images, we propose a phenomenological theory to explain the observations.