Unpinning the spiral waves by using parameter waves

The spiral waves anchored to heterogeneous areas are more difficult to control and eliminate than freely rotating ones in homogenous mediums. To eliminate pinned spiral waves, the resistant force should be provided to resist the pinning force. Other than advection field, we introduce parametric wave to play the role of providing resistant force. It is found that the parametric wave with large enough amplitude and proper frequency can unpin and eliminate the spiral wave successfully. The capability of parametric wave in providing resistant force is dependent on its amplitude and frequency sensitively. On the basis of parametric wave, the dependence of pinning force on the size and level of heterogeneity is further confirmed.     

External forcing of spiral waves

The effect of an external rhythm on rotating spiral waves in excitable media is investigated. Parameters of the unperturbed medium were chosen, such that the organizing spiral tip describes meandering (hypocyclic) trajectories, which are the most general shape for the experimentally observed systems. Periodical modulation of excitability in a model of the Belousov-Zhabotinsky (BZ) reaction forces meandering spiral tips to describe trajectories that are not found at corresponding stationary conditions. For different modulation periods, two types of resonance drift, phase-locked tip motion, a spectrum of hypocyclic trajectories, and complex multifrequency patterns were computed. The computational results are complemented by experimental data obtained for periodically changing illumination of the photosensitive BZ reaction. The observed drastic deformation of the tip trajectory is considered as an efficient means to study and to control wave processes in excitable media.     

Partial waves in coupled spiral lines

The slow-wave system consists of two parallel spirals of rectangular cross section wound on insulating rods; the mode of winding and excitation conditicns may vary. The field expressions and dispersion equations are derived for four possible cases. The results can be used to choose a slow-wave system with given dispersion features.     

Kinematics of rigidly rotating spiral waves

Spiral waves rigidly rotating in excitable media are studied by use of a free-boundary approach. This study reveals the selection principle which determines the shape and the rotation frequency of spiral waves in an unbounded medium with a given excitability. It is shown that a rigidly rotating spiral in a medium with a strongly reduced refractoriness is supported within a range of the medium excitability restricted by two universal limits. At the low excitability limit the spiral core radius diverges, while at the high excitability limit it vanishes. The simulations performed for the medium excitability higher than the high excitability limit reveal nonstationary rotating waves, which considerably differ from well-studied meandering spiral waves. It is shown how the proposed free-boundary approach can be extended to the case of an arbitrary refractoriness. The predictions of the free-boundary approach are in good agreement with the results from numerical simulations of the underlying reaction-diffusion model and with asymptotics derived earlier for highly and weakly excitable media.     

Light induced annihilation and shift of spiral waves

The light-induced collapse of a pair of spiral waves was studied in a chemically active medium based on the photosensitive Ru(bpy)(3)-catalyzed Belousov-Zhabotinsky reaction. Spiral waves annihilate only if the light intensity is increased in proper phase relative to the spiral waves' rotation. Otherwise, the distance between spiral wave cores increases and the pair survives. Computer simulations reveal the mechanism which forces the spiral waves to collide and annihilate. It is based on the shift of a single spiral wave upon an instantaneous decrease of excitability of the medium. (c) 1996 American Institute of Physics.     

Superspiral structures of meandering and drifting spiral waves

The spatiotemporal superstructure of meandering and drifting spiral waves is explained analytically. It is also demonstrated that the Hopf eigenmode that causes the transition to meandering waves is weakly exponentially localized at onset but grows exponentially slightly before onset.     

Surface spiral waves in a filamentary vortex

Second-order [ O(k(2)), k = omega/c] nondipole effects in soft-x-ray photoemission are demonstrated via an experimental and a theoretical study of angular distributions of neon valence photoelectrons in the 100-1200 eV photon-energy range. A newly derived theoretical expression for nondipolar angular distributions characterizes the second-order effects using four new parameters with primary contributions from pure-quadrupole and octupole-dipole interference terms. Independent-particle calculations of these parameters account for a significant portion of the existing discrepancy between experiment and theory for Ne 2p first-order nondipole parameters.     

Nonlinear spiral waves in a galactic disk

An analytical solution of the nonlinear dynamic equations for a galactic disk is found. This solution describes the spiral design of spiral galaxies. The logarithmic profile of the spiral design and relatively larger density fluctuations as compared to velocity-field fluctuations are explained. Breaking of the obtained solution takes place for a certain critical amplitude. This can be a mechanism for the formation of galactic shocks and narrow star formation regions.     

The mixed PDE for amplifying spiral waves

A special class of solutions of the wave equations is determined by a mixed-type PDE. Two kinds of well-posed boundary-value problems are solved. The equation has the following interesting property: it is a mixed equation of the first class and behaves as a mixed equation of the second class in large regions.Dedicated to Professor L. K. Hua.     

FitzHugh-Nagumo系统中螺旋波的控制

采用FitzHugh-Nagumo方程,研究了二维时空系统中螺旋波的控制问题,利用相空间压缩方法对部分系统变量的振幅进行限制从而影响螺旋波的稳定性.研究表明,控制过程可分为三个不同的阶段:在较小压缩限条件下螺旋波可以被完全消除,系统进入均匀定态;在较大的压缩限条件下螺旋波能够稳定存在,而且其振荡频率不随控制参数的改变而发生变化;当压缩限介于上述两者之间时,系统表现为时空混沌态.对上述控制过程进行了进一步的讨论,研究了不同控制参数条件下的系统斑图、变量的演化、相空间轨道等性质,并且对振幅函数和振荡频率特征进 关键词： 螺旋波 相空间压缩 FitzHugh-Nagumo方程     

非均匀可激发介质中的稀密螺旋波

在非均匀可激发介质中,采用Barkley模型数值模拟了稀螺旋波和密螺旋波, 并对二者的动力学行为随参数的变化进行了研究. 结果发现:稀螺旋波的旋转频率随参数b的增加迅速减小,之后趋于饱和, 显示出不同于密螺旋波的行为;两种螺旋波的周期和波长随参数ε 和非均匀区域尺寸R的增加而增加,相对稀螺旋波而言,密螺旋波的性质对R的依赖更为敏感; 稀螺旋波端点的波速随R的增加而减小,与密螺旋波波速变化趋势相反. 另外,由于非均匀区域的影响,当ε 或b 超过某一临界值时,螺旋波臂上出现缺陷点.     

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.     

Synchronizing spiral waves in a coupled Rossler system

The synchronisation of spiral patterns in a drive-response R6ssler system is studied. The existence of three types of synchronisation is revealed by inspecting the coupling parameter space. Two transient stages of phase synchronisation and partial synchronisation are observed in a comparatively weak feedback coupling parameter regime, whilst complete synchronisation of spirals is found with strong negative couplings. Detailed observations of the synchronous process, such as oscillatory frequencies, parameters mismatches and amplitude variations, etc, are investigated via numerical simulations.     

Rotating spiral waves in a modified Fitz-Hugh-Nagumo model

A modified Fitz-Hugh-Nagumo model (a two-variable reaction-diffusion system with an excitable kinetics and a diffusing fast variable) was used to study numerically the rotating waves in a circular domain and in a two-dimensional ring. Large deviations from a Wiener type of behaviour of rotating spiral waves were revealed. We have shown that there are conditions under which: (i) vortices can appear in a medium with a hole but do not exist in a disk; (ii) two kinds of vortices with considerably differing periods can occur in the same ring; (iii) there is a non-monotonic dependence of vortex period on the hole size. These phenomena are believed to take place in myocardial tissue and in chemical active media. The conditions under which they could be observed experimentally are discussed.     

Projective synchronization of two coupled excitable spiral waves

Interaction of two identical excitable spiral waves in a bilayer system is studied. We find that the two spiral waves can be completely synchronized if the coupling strength is sufficiently large. Prior to the complete synchronization, we find a new type of weak synchronization between the two coupled systems, i.e., the spiral wave of the driven system has the same geometric shape as the spiral wave of the driving system but with a much lower amplitude. This general behavior, called projective synchronization of two spiral waves, is similar to projective synchronization of two coupled nonlinear oscillators, which has been extensively studied before. The underlying mechanism is uncovered by the study of pulse collision in one-dimensional systems.     

Motion of spiral waves induced by local pacing

The motion of spiral waves in excitable media driven by a weak pacing around the spiral tip is investigated numerically as well as theoretically. We presented a Bifurcations diagram containing four types of the spiral motion induced by different frequencies of pacing: rigidly rotating, inward-petal meandering, resonant drift, and outward-petal meandering spiral. Simulation shows that the spiral resonantly drifts when the frequency of pacing is close to that of the spiral rotation. We also find that the speed and direction of the drift can be efficiently controlled by means of the strength and phase of the local pacing, which is consistent with analytical results based on the framework of the weak deformation approximation.      

Nonstationary rotation of spiral waves: Three-dimensional effect

Nonstationary rotation of spiral waves was studied in experiments with the chemical active medium (the Belousov-Zhabotinsky reaction). It was shown that nonstationarity in some cases is a result of nonuniformity of the reaction throughout the solution depth due to nonuniform saturation with oxygen from the surface to bottom of the solution. Numerical experiments confirm the experimental data. It was shown numerically that this type of nonuniformity can lead to nonstationary rotation of spiral waves.