Stabilization of spiral wave and turbulence in the excitable media using parameter perturbation scheme

This paper proposes a scheme of parameter perturbation to suppress the stable rotating spiral wave, meandering spiral wave and turbulence in the excitable media, which is described by the modified Fitzhug-Nagumo （MFHN） model. The controllable parameter in the MFHN model is perturbed with a weak pulse and the pulse period is decided by the rotating period of the spiral wave approximatively. It is confirmed that the spiral wave and spiral turbulence can be suppressed greatly. Drift and instability of spiral wave can be observed in the numerical simulation tests before the whole media become homogeneous finally.     

非均匀可激介质中的螺旋波

以Barkley模型为对象,研究了可激介质的非均匀性对螺旋波斑图形成的影响.该模型中各参数与可激介质的属性密切相关,通过参数涨落的正态分布来刻画非均匀性,数值研究了单参数以及多参数涨落的正态分布情形下螺旋波斑图的形成.研究表明,可激介质的非均匀性对于螺旋波波纹的粗细及疏密程度有较大影响.参数涨落分布的方差越大,形成的螺旋波波纹越粗糙.对于两参数均匀分布的极端情形,当参数分布大于某一范围,无法形成螺旋波.这些都与螺旋波旋转的角频率密切相关.螺旋波旋转的角频率越大,螺旋波波纹越粗,同时波纹越密集;反之,螺旋波 关键词： 螺旋波 非均匀介质 Barkley模型     

Suppression of Spiral Wave in Modified Orengonator Model

In this paper, a spatial perturbation scheme is proposed to suppress the spiral wave in the modified Orengonator model, which is used to describe the chemical reaction in the light-sensitive media. The controllable external illumination Φ is perturbed with a spatial linear function. In our numerical simulation, the scheme is investigated by imposing the external controllable illumination on the space continuously and/or intermittently. The numerical simulation results confirm that the stable rotating spiral wave still can be removed with the scheme proposed in this paper even if the controllable Φ changed vs. time and space synchronously. Then the scheme is also used to control the spiral wave and turbulence in the modified Fitzhugh-Nagumo model. It is found that the scheme is effective to remove the sable rotating and meandering spiral wave but it costs long transient period and intensity of the gradient parameter to eliminate the spiral turbulence.     

时变反应扩散系统中螺旋波和湍流的控制

研究了一类参数时变的反应扩散系统中螺旋波和湍流对外电场的响应问题.在数值模拟中,以一类改进的Fitzhugh-Nagumo模型为研究对象(在恰当参数值下可分别描述激发介质和振荡介质),考虑随机和不确定因素(如内外噪声、气压、温度梯度分布和介质形变等)所引起的系统参数涨落对斑图演化的影响,在模拟中选取的参数涨落范围确保系统可以观测到稳定旋转的螺旋波、漫游的螺旋波和湍流,经历一定的暂态过程后,对介质施加极化电场,研究螺旋波和湍流在外电场中的演化.数值计算结果表明：在系统参数发生涨落和外电场强度比较小情况下,主 关键词： 螺旋波 湍流 时变系统 Fitzhugh-Nagumo模型     

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.     

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.     

Novel type of amplitude spiral wave in a two-layer system

Interaction of spiral waves in a two-layer system described by a model of coupled complex Ginzburg-Landau equations with negative-feedback couplings ε(1) and ε(2) is studied. Synchronization of two spiral waves can be broadly found if ε(1)+ε(2) is sufficiently large. Prior to the synchronization, under the condition of strongly asymmetric coupling (∣ε(1)-ε(2)∣?0), a novel type of spiral wave, amplitude spiral wave, exists in the driven system. The pattern of amplitude spiral wave shows the spiral in the amplitude and without a singularity point (tip), compared to usual spiral waves known for phase with amplitude uniform far away from tips and rotating around tips.     

Kinetic Monte Carlo simulations of travelling pulses and spiral waves in the lattice Lotka-Volterra model

Kinetic Monte Carlo simulations are used to study the stochastic two-species Lotka-Volterra model on a square lattice. For certain values of the model parameters, the system constitutes an excitable medium: travelling pulses and rotating spiral waves can be excited. Stable solitary pulses travel with constant (modulo stochastic fluctuations) shape and speed along a periodic lattice. The spiral waves observed persist sometimes for hundreds of rotations, but they are ultimately unstable and break-up (because of fluctuations and interactions between neighboring fronts) giving rise to complex dynamic behavior in which numerous small spiral waves rotate and interact with each other. It is interesting that travelling pulses and spiral waves can be exhibited by the model even for completely immobile species, due to the non-local reaction kinetics.     

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.     

Spiral Wave in Small-World Networks of Hodgkin--Huxley Neurons

The effect of small-world connection and noise on the formation and transitionof spiral wave in the networks of Hodgkin-Huxley neurons are investigated in detail. Some interesting results are found in our numerical studies. i) The quiescent neurons are activated to propagate electric signal to others by generating and developing spiral wave from spiral seed in small area. ii) A statistical factor is defined to describe the collective properties and phase transition induced by the topology of networks and noise. iii) Stable rotating spiral wave can be generated and keeps robust when the rewiring probability is below certain threshold, otherwise, spiral wave can not be developed from the spiral seed and spiral wave breakup occurs for a stable rotating spiral wave. iv) Gaussian white noise is introduced on the membrane of neuronsto study the noise-induced phase transition on spiral wave in small-world networks of neurons. It is confirmed that Gaussian white noise plays active role in supporting and developing spiral wave in the networks of neurons, and appearance of smaller factor of synchronization indicates high possibility to induce spiral wave.     

Selection of spiral waves in excitable media with a phase wave at the wave back

Universal relationships between the medium excitability and the angular velocity and the core radius of rigidly rotating spiral waves in excitable media are derived for situations where the wave front is a trigger wave and the wave back is a phase wave. Two universal limits restricting the region of existence of spiral waves in the parameter space are demonstrated. The predictions of the free-boundary approach are in good quantitative agreement with results from numerical reaction-diffusion simulations performed on the Kessler-Levine model.     

无扩散功能的缺陷对螺旋波动力学行为的影响

采用Br 模型,在二维激发介质中引入无扩散功能的缺陷,研究了均匀分布的缺陷对螺旋波动力学行为的影响.研究发现,缺陷导致介质的激发性降低、波传播速度减少,在一定数量的缺陷均匀分布下,缺陷可以使原来稳定的螺旋波发生漫游或破碎,缺陷使原来不稳定的螺旋波稳定或漫游,首次在激发介质中观察到螺旋波因Doppler效应破碎形成小螺旋波和时空混沌共存现象.对产生这些现象的物理机理做了简要的讨论. 关键词： 激发介质 螺旋波 缺陷     

Controlling intracellular Ca2+ spiral waves by the local agonist in the cell membrane

A modified spatially extended Tang-Othmer Ca2+ model is used to study intracellular Ca2+ spiral waves numerically.It is found that,as a local stimulation,the local agonist-binding on the cell membrane,which enhances the local concentration of the messenger molecule inositol 1,4,5-trisphosphate(IP 3),can influence the dynamics of the spiral waves.1) Strong enough stimuli can change the spiral wave from a meandering to a rigidly rotating one.2) On the other hand,strong enough stimuli can suppress the spiral wave from the system.It provides the theoretical clue for controlling the spiral waves by stimulating the cell membrane.     

Dynamics of spiral waves under phase feedback control in a Belousov-Zhabotinsky reaction

Feedback control of spiral waves by the phases of the spiral tip is investigated experimentally in a light-sensitive Belousov-Zhabotinsky reaction. The phases of rotation (Psi(r)) and meandering (Psi(m)) of the spiral tip are obtained in real time during experiments. It is found that, for both meandering and rigid rotating spirals, one can manipulate the spirals to move with any arbitrary paths by the feedback signals derived from Psi(r). Synchronization between meandering and rotation dynamics can be induced when both Psi(m) and Psi(r) are used simultaneously as control signals. Experimental findings are compared well with numerical simulations of the Oregonator model.     

Instability and Death of Spiral Wave in a Two-Dimensional Array of Hindmarsh-Rose Neurons

Spiral wave could be observed in the excitable media, the neurons are often excitable within appropriate parameters. The appearance and formation of spiral wave in the cardiac tissue is linked to monomorphic ventricular tachycardia that can denervate into polymorphic tachycardia and ventricular fibrillation. The neuronal system often consists of a large number of neurons with complex connections. In this paper, we theoretically study the transition from spiral wave to spiral turbulence and homogeneous state （death of spiral wave） in two-dimensional array of the Hindmarsh-Rose neuron with completely nearest-neighbor connections. In our numerical studies, a stable rotating spiral wave is developed and selected as the initial state, then the bifurcation parameters are changed to different values to observe the transition from spiral wave to homogeneous state, breakup of spiral wave and weak change of spiral wave, respectively. A statistical factor of synchronization is defined with the mean field theory to analyze the transition from spiral wave to other spatial states, and the snapshots of the membrane potentials of all neurons and time series of mean membrane potentials of all neurons are also plotted to discuss the change of spiral wave. It is found that the sharp changing points in the curve for factor of synchronization vs. bifurcation parameter indicate sudden transition from spiral wave to other states. And the results are independent of the number of neurons we used.     

气体放电系统中多臂螺旋波的数值分析

采用Purwins的三变量模型, 在二维空间对气体放电系统中多臂螺旋波的形成和转化进行了数值研究. 通过分析方程参数对系统空间的影响, 确定了系统获得稳定螺旋波的参数空间; 得到了斑图由简单静态六边形到螺旋波的演化过程, 分析了螺旋波的形成机制和时空特性; 进一步获得六种不同臂数的多臂螺旋波斑图(例如: 双臂、三臂、四臂、五臂、六臂和七臂螺旋波). 结果表明: 螺旋波斑图出现在图灵-霍普夫(Turing-Hopf)空间, 是Turing模和Hopf模相互竞争、相互作用的结果; 不同臂数的螺旋波波头均在持续地旋转运动, 其运动速度随螺旋波臂数的增加而增大; 随着螺旋波臂数的增加, 其波头的运动形式愈加复杂; 由于受微扰及边界条件的影响, 多臂螺旋波可以向臂数少一的螺旋波发生转变, 数值模拟结果与实验结果符合较好. 关键词： 螺旋波 数值模拟 气体放电     

Spontaneous spiral wave breakup caused by pinning to the tissue defect

The work presents a mechanism of spiral wave initiation due to the specific boundary conditions on a border of cardiac tissue defect. There are known scenarios when anatomical or functional defects in cardiac tissue may provoke the spiral wave origination, including unidirectional blockage while passing through the narrow gates, bent over critical curvature wave fronts, inhomogeneous recovery of the tissue, etc. We show a new scenario of spiral wave breakup on a small defect, which is unexcitable but permeable for ionic currents supporting the excitation wave. It was believed that such defects stabilize the rotating wave; however, as shown, instead of stabilizing it leads to the spiral breakup and subsequent multiplication of the rotating waves.     

Accelerating electromagnetic magic field from the C-metric

Various aspects of the C-metric representing two rotating charged black holes accelerated in opposite directions are summarized and its limits are considered. A particular attention is paid to the special-relativistic limit in which the electromagnetic field becomes the “magic field” of two oppositely accelerated rotating charged relativistic discs. When the acceleration vanishes the usual electromagnetic magic field of the Kerr–Newman black hole with gravitational constant set to zero arises. Properties of the accelerated discs and the fields produced are studied and illustrated graphically. The charges at the rim of the accelerated discs move along spiral trajectories with the speed of light. If the magic field has some deeper connection with the field of the Dirac electron, as is sometimes conjectured because of the same gyromagnetic ratio, the “accelerating magic field” represents the electromagnetic field of a uniformly accelerated spinning electron. It generalizes the classical Born’s solution for two uniformly accelerated monopole charges.