The influence of long-range links on spiral waves and their application for control

The influence of long-range links on spiral waves in an excitable medium has been investigated.Spatiotemporal dynamics in an excitable small-world network transform remarkably when we increase the long-range connection probability P.Spiral waves with few perturbations,broken spiral waves,pseudo spiral turbulence,synchronous oscillations,and homogeneous rest state are discovered under different network structures.Tip number is selected to detect non-equilibrium phase transition between different spatiotemporal patterns.The Kuramoto order parameter is used to identify these patterns and explain the emergence of the rest state.Finally,we use long-range links to successfully control spiral waves and spiral turbulence.     

Self-sustained target waves in excitable media with only a long-range link

In this paper we investigate spatiotemporal pattern formation in excitable media with only a long-range link. Besides the trivial solutions of spiral patterns, we find the asymptotic self-sustained target waves in the autonomous tissues. The wave source supporting this kind of new pattern is the oscillatory one-dimensional Winfree-loop self-organized under the presence of a long-range link, which is explored by the dominant phase-advanced driving method. Based on this understanding we can effectively regulate the oscillations of excitable media by suitably arranging the long-range link, including construction of self-sustained target waves with controllable period and wave length, or manipulation of system states between different patterns.     

时空调制对可激发介质螺旋波波头动力学行为影响及控制研究

本文首先研究了时空调制对可激发介质中周期螺旋波波头动力学行为的影响. 随着时空调制的增大, 螺旋波经历了周期螺旋波、外滚螺旋波、旅行螺旋波和内滚螺旋波的显著变化. 通过定义序参量来定量的描述由时空调制引起的螺旋波在不同态之间非平衡跃迁的临界条件, 及漫游螺旋波波头圆滚圆半径随调制参数的变化情况. 当时空调制增大到某个临界值时, 螺旋波发生了破碎; 再增加时空调制, 螺旋波则发生了衰减, 系统最终演化为空间均匀静息态. 在文中给出了螺旋波发生破碎和衰减的机理和原因. 最后将时空调制方法运用于漫游螺旋波, 实现了将漫游螺旋波控制成周期螺旋波, 或将其控制为空间均匀静息态.     

Suppression of spiral waves using intermittent local electric shock

In this paper, an intermittent local electric shock scheme is proposed to suppress stable spiral waves in the Barkley model by a weak electric shock (about 0.4 to 0.7) imposed on a random selected n×n grids (n=1-5, compared with the original 256×256 lattice) and monitored synchronically the evolutions of the activator on the grids as the sampled signal of the activator steps out a given threshold (i.e., the electric shock works on the n×n grids if the activator u\leq0.4 or u \geq 0.8). The numerical simulations show that a breakup of spiral is observed in the media state evolution to finally obtain homogeneous states if the electric shock with appropriate intensity is imposed.     

用同步复极化终止心脏中的螺旋波和时空混沌

为了模拟电击除颤导致动作电位持续时间缩短, 在Luo-Rudy相I心脏模型中引入了同步复极化. 研究了同步复极化对螺旋波和时空混沌动力学的影响. 数值结果表明: 在控制周期比较小的情况下, 同步复极化可以有效消除螺旋波和时空混沌, 在有一些控制参数下, 同步复极化只能消除螺旋波, 或者只能消除时空混沌. 当螺旋波不被控制时, 观察到螺旋波转变为长周期和长波长的螺旋波或破碎成时空混沌的现象. 并对控制机制进行了分析. 关键词： 螺旋波 时空混沌 同步复极化 控制     

用晶格玻尔兹曼方法研究螺旋波的产生机制和演化行为

采用五速正方晶格玻尔兹曼模型，由晶格玻尔兹曼方程推导得到了反应扩散方程.分析了Selkov反应扩散系统螺旋波的形成机制.零流边界条件下计算机数值模拟螺旋波的形成和破碎过程，发现Selkov反应扩散系统的失稳属于Doppler失稳.改变参数模拟系统的演化行为，发现不同的参数下系统可能到达三种不同的状态：均匀定态、混沌状态和螺旋波. 关键词： 晶格玻尔兹曼方法 螺旋波 计算机模拟     

极化电场对可激发介质中螺旋波的控制

螺旋波在不同的物理、化学和生物系统中普遍存在.周期外场,比如极化电场,尤其是具有旋转对称性的圆极化电场可对螺旋波动力学产生重要影响.本文综述了极化电场对可激发介质中螺旋波的控制,包括共振漂移、同步、手征对称性破缺、多臂螺旋波的稳定、次激发介质中的螺旋波、三维回卷波湍流态的控制、心脏组织中螺旋波的去钉扎、心脏组织中螺旋波湍流态的控制等.     

耦合可激发介质中螺旋波的控制研究

采用Br模型研究了三层耦合可激发介质中螺旋波的控制.相邻层之间采用双向耦合.利用加在第二层介质上的局域周期信号产生的平面波来消除螺旋波.数值模拟表明:只有当三层介质的耦合满足一定条件才可能实现螺旋波的控制,可以通过耦合互补方式实现螺旋波的控制;平面波与低频螺旋波的相互作用可以产生高频螺旋波,导致螺旋波不能被消除;存在优化的驱动宽度,过大或过小的驱动宽度需要增加第一、三层介质的耦合强度.观察到控制结果依赖控制时机的现象.研究结果可用于植入式心脏除颤器的设计.     

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.     

Synchronization of spiral waves in a two-layer coupled inhomogeneous excitable system

We studied synchronization behaviours of spiral waves in a two-layer coupled inhomogeneous excitable system. It was found that phase synchronization can be observed under weak coupling strength. By increasing the coupling strength, the synchronization is broken down. With the further increase of the coupling strength, complete synchronization and phase synchronization occur again. We also found that the inhomogeneity in excitable systems is helpful to the synchronization.     

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.     

心脏中的螺旋波和时空混沌的抑制研究

以Luo-Rudy相I心脏模型为基础,研究心脏中螺旋波和时空混沌的控制,提出了两种控制方法: (Ⅰ)通过交替改变细胞外钾离子浓度来产生平面波,再利用弱外电场辅助平面波抑制螺旋波和时空混沌; (Ⅱ)先提高细胞外钾离子浓度,然后利用外电场激发波的方式产生平面波,再用平面波去抑制螺旋波和时空混沌. 研究结果表明,只要适当选择控制参数,这两种方法都能够有效抑制螺旋波和时空混沌. 当心肌出现局部缺血时,在心肌缺血处就会出现高的细胞外钾离子浓度,在这种情况下, 可以采用电场发射波的方法来抑制心脏中的螺旋波和时空混沌.对这些控制方法的优点和控制机制做了解释.     

用钙离子通道激动剂抑制心脏组织中的螺旋波和时空混沌

本文以LuoRudy91模型为基础,研究心脏组织中的螺旋波和时空混沌的抑制.提出应用钙离子通道激动剂来提高慢速内行钙离子流的最大电导率—Gsi,达到抑制螺旋波和时空混沌的目的.研究结果表明:该方法可以有效抑制心脏组织中的螺旋波和时空混沌,即使系统出现含时外行钾离子流的最大电导率—GK分布不均匀,该控制方法仍然有效.对控制机理进行了分析.     

Elimination of spiral waves and spatiotemporal chaos by the synchronization transmission technology of network signals

A method to eliminate spiral waves and spatiotemporal chaos by using the synchronization transmission technology of network signals is proposed in this paper. The character of the spiral waves and the spatiotemporal chaos in the Fitzhugh—Nagumo model is presented. The network error evolution equation with spatiotemporal variables and the corresponding eigenvalue equation are determined based on the stability theory, and the global synchronization condition is obtained. Simulations are made in a complex network with Fitzhugh—Nagumo models as the nodes to verify the effectiveness of the synchronization transmission principle of the network signal.     

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.     

长程电子关联对聚合物中激子极化率的影响

本文研究了在外电场下高分子的线性极化率和三阶非线性极化率,发现电子电子相互作用使激子线性极化率和三阶非线性极化率都降低,而长程电子关联效应的作用更进一步降低 和。准确地计算高分子聚合物的极化率可以更好的理解共轭聚合物的长程电子关联对有机分子线性和非线性响应的影响,确定其结构与非线性光学性质的关系。     

长程电子关联对聚合物中激子极化率的影响

本文研究了在外电场下高分子的线性极化率和三阶非线性极化率,发现电子-电子相互作用使激子线性极化率χ(1)xx和三阶非线性极化率χ(3)xxxx都降低,而长程电子关联效应的作用更进一步降低χ(1)xx和χ(3)xxxx.准确地计算高分子聚合物的极化率可以更好的理解共轭聚合物的长程电子关联对有机分子线性和非线性响应的影响,确定其结构与非线性光学性质的关系.     

Control of spiral waves and turbulent states in a cardiac model by travelling—wave perturbations

We propose a travelling-wave perturbation method to control the spatiotemporal dynamics in a cardiac model.It is numerically demonstrated that the method can successfully suppress the wave instability(alternans in action potential duration) in the one-dimensional case and converty spiral waves and turbulent states to the normal travelling wave states in the two-dimensional case.An experimental scheme is suggested which may provide a new design for a cardiac defibrillator.     

The effect of cellular aging on the dynamics of spiral waves

Cellular aging can result in deterioration of electrical coupling, the extension of the action potential duration, and lower excitability of the cell. Those factors are introduced into the Greenberg–Hastings cellular automaton model and the effects of the cellular aging on the dynamics of spiral waves are studied. The numerical results show that a 50% reduction of the coupling strength of aging cells has a little influence on spiral waves. If the coupling strength of aging cells equals zero, the ability for the medium to maintain spiral waves will be reduced by approximately 50% when the aging cell ratio increases from 0 to 0.5, where the reduction of cell excitability plays a major role in inducing disappearance of spiral waves. When the relevant parameters are properly chosen, the cellular aging can lead to the meandering of spiral waves,the emergence of the binary spiral waves, and even the disappearance of spiral waves via the stopping rotation or shrinkage of wave. Physical mechanisms of the above phenomena are analyzed briefly.     

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