Oscillation sources and wave propagation paths in complex networks consisting of excitable nodes

Self-sustained oscillations in complex networks consisting of nonoscillatory nodes have attracted long-standing interest in diverse natural and social systems. We study the self-sustained periodic oscillations in random networks consisting of excitable nodes. We reveal the underlying dynamic structure by applying a dominant phase-advanced driving method. The oscillation sources and wave propagation paths can be illustrated clearly via the dynamic structure revealed. Then we are able to control the oscillations with surprisingly high efficiency based on our understanding.     

Network dynamics and its relationships to topology and coupling structure in excitable complex networks

All dynamic complex networks have two important aspects, pattern dynamics and network topology. Discovering different types of pattern dynamics and exploring how these dynamics depend or/network topologies are tasks of both great theoretical importance and broad practical significance. In this paper we study the oscillatory behaviors of excitable complex networks （ECNs） and find some interesting dynamic behaviors of ECNs in oscillatory probability, the multiplicity of oscillatory attractors, period distribution, and different types of oscillatory patterns （e.g., periodic, quasiperiodic, and chaotic）. In these aspects, we further explore strikingly sharp differences among network dynamics induced by different topologies （random or scale-free topologies） and different interaction structures （symmetric or asymmetric couplings）. The mechanisms behind these differences are explained physically.     

两层耦合可激发介质中螺旋波转变为平面波

采用Br-Eiswirth模型研究了两层耦合可激发介质中螺旋波的动力学,两层介质通过网络连接,即在每一层介质上,每一列选一个可激发单元作为中心点,在一层介质上同一列的可激发单元只与另一层介质上对应的中心点及其8个邻居有耦合.数值模拟结果表明:通过这种局部耦合,在适当小的耦合强度下两耦合螺旋波可实现同步,增大耦合强度会导致螺旋波漫游和漂移,造成螺旋波不同步,观察到螺旋波与静息态、低频平面波和不规则斑图共存现象.在适当强的耦合强度下,还观察到两螺旋波转变成同步的平面波消失现象.对产生这些现象的物理机理做了讨论.     

三维可激发系统中Winfree湍流态的控制

三维可激发系统中的Winfree湍流态被认为与心室纤维性颤动可能有着密切的关系.如何快速而有效地消除Winfree湍流是理论工作者非常关心的问题.文章作者发展了两种可有效地控制三维可激发系统中Winfree湍流态的方法：（1）局域的周期刺激,即通过小区域内的周期刺激所产生的激发波来消除Winfree湍流;（2）全局的时空微扰,通过对参数的时空调制来消除Wnifree湍流.     

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     

Feedback control of wave segments in an excitable medium

Depending on the excitability of the medium, a propagating wave segment will either contract or expand to fill the medium with spiral waves. This paper aims to introduce a simple mechanism of feedback control to stabilize such an expansion or contraction. To do this, we lay out a feedback control system in a block diagram and reduce it into a bare, universal formula. Analytical and experimental findings are compared through a series of numerical simulations of the Barkley model.     

可激发介质中环形异质介质导致自维持靶波

在二维可激发介质中引入环形异质可激发介质,研究了可激发介质中自维持靶波的形成,数值模拟结果表明:当介质的激发性和环的尺寸适当选取时,初始的扰动可在可激发介质中产生自维持靶波,对产生自维持靶波的物理机理作了讨论.     

Cluster synchronization and spatio-temporal dynamics in networks of oscillatory and excitable Luo-Rudy cells

We study collective phenomena in nonhomogeneous cardiac cell culture models, including one- and two-dimensional lattices of oscillatory cells and mixtures of oscillatory and excitable cells. Individual cell dynamics is described by a modified Luo-Rudy model with depolarizing current. We focus on the transition from incoherent behavior to global synchronization via cluster synchronization regimes as coupling strength is increased. These regimes are characterized qualitatively by space-time plots and quantitatively by profiles of local frequencies and distributions of cluster sizes in dependence upon coupling strength. We describe spatio-temporal patterns arising during this transition, including pacemakers, spiral waves, and complicated irregular activity.     

非均匀激发介质中螺旋波的演化

采用简单的离散可激发介质模型研究了不同性质和形状的小异质性颗粒对螺旋波演化的影响,在小异质性颗粒均匀分布的情况下,螺旋波的失稳与小异质性颗粒的形状、分布密度和性质有关.数值研究结果表明:在适当的条件下,可以观察到稳定螺旋波发生漫游和螺旋波漂移出系统边界现象,首次观察到螺旋波破碎成空间无序的周期变化斑图和破碎成时空有序的迷宫斑图现象,简要讨论了产生这些现象的物理机理.     

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.     

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.     

可激发介质湍流的耦合同步及控制

利用相互耦合方法实现了两个处于湍流态的可激发系统的精确同步，给出了确定耦合系数的方法，计算了最大横向Lyapunov指数.并基于相互耦合，将处于湍流态的可激发系统与两个处于不同状态的可激发系统进行相互耦合，实现了用两种不同方法对湍流态的稳定控制. 关键词： 可激发介质 湍流控制 同步 耦合系数     

三层弱循环耦合可激发介质中螺旋波动力学

采用Bär模型研究了具有循环反馈耦合的三层可激发介质中的螺旋波动力学行为,数值模拟结果显示: 在耦合强度较小时, 在各子系统中可观察到螺旋波漂移或漫游; 当耦合强度稍大时, 相互作用既可以使螺旋波漫游或漂移出系统边界而使子系统回到静息态,还可以使子系统的螺旋波态转变为靶波或湍流态, 并观察到子系统的渐近态依赖初值现象; 继续增大耦合强度, 三个子系统的螺旋波可达到近似广义同步; 当耦合强度更大时, 螺旋波演化为湍流态.     

用元胞自动机模型研究二维激发介质中的非线性波

采用Greenberg-Hasting元胞自动机模型研究了激发介质中非线性波的有关性质：在零流边界条件下根据计算机数值模拟研究了行波波速随邻域半径、激发阈值的变化关系,分析得到激发介质的激发条件;同时模拟研究了螺旋波波头轨迹受不应态数和激发阈值的影响并分析产生这些影响的内在微观机理. 关键词： 元胞自动机 激发介质 非线性波     

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.     

Attractive target wave patterns in complex networks consisting of excitable nodes

This review describes the investigations of oscillatory complex networks consisting of excitable nodes,focusing on the target wave patterns or say the target wave attractors.A method of dominant phase advanced driving(DPAD) is introduced to reveal the dynamic structures in the networks supporting oscillations,such as the oscillation sources and the main excitation propagation paths from the sources to the whole networks.The target center nodes and their drivers are regarded as the key nodes which can completely determine the corresponding target wave patterns.Therefore,the center(say node A) and its driver(say node B) of a target wave can be used as a label,(A,B),of the given target pattern.The label can give a clue to conveniently retrieve,suppress,and control the target waves.Statistical investigations,both theoretically from the label analysis and numerically from direct simulations of network dynamics,show that there exist huge numbers of target wave attractors in excitable complex networks if the system size is large,and all these attractors can be labeled and easily controlled based on the information given by the labels.The possible applications of the physical ideas and the mathematical methods about multiplicity and labelability of attractors to memory problems of neural networks are briefly discussed.     

激发介质中螺旋波失稳的微观机理研究

采用晶格Boltzmann方法研究了激发介质中螺旋波的失稳,计算机数值模拟给出了激发介质中螺旋波失稳前后的速度场分布,并结合斑图和波头轨迹进行讨论发现,稳定螺旋波的速度场分布表现为螺旋波旋转中心处的速度做周期突变;在螺旋波开始失稳时,速度场分布表现为该位置粒子速度突变加快最后变得无规律,使速度集团分解无规律,导致速度场分布越来越混乱,并最终使系统进入时空混沌态. 关键词： 晶格Boltzmann方法 激发介质 螺旋波 时空混沌     

Adaptive approach to global synchronization of directed networks with fast switching topologies

Global synchronization of directed networks with switching topologies is investigated. It is found that if there exists at least one directed spanning tree in the network with the fixed time-average topology and the time-average topology is achieved sufficiently fast, the network will reach global synchronization for appreciate coupling strength. Furthermore, this appreciate coupling strength may be obtained by local adaptive approach. A sufficient condition about the global synchronization is given. Numerical simulations verify the effectiveness of the adaptive strategy.     

非对称耦合两层可激发介质中的螺旋波动力学

本文采用Bär-Eiswirth模型研究了两层可激发介质中螺旋波的动力学, 两层介质采用抑制和兴奋性非对称耦合. 数值模拟结果表明: 兴奋性非对称耦合可以促进两个不同频率的螺旋波锁频, 即使初始频率相差大, 两螺旋波也能实现锁频, 这种耦合使两个螺旋波具有最强的锁频能力; 当两层介质采用抑制性非对称耦合时, 只有当两个初始螺旋波的频率差比较小才能实现锁频, 而且比一般扩散耦合的锁频范围窄, 两螺旋波锁频能力达到最低水平; 当耦合强度和控制参数适当选取时, 抑制性和兴奋性非对称耦合既可以使其中一层介质维持螺旋波态, 使另一层介质中的螺旋波演化到静息态或低频靶波态, 也可以使两层介质中的螺旋波都漫游, 或都转变成靶波, 最后这两个靶波要么消失, 要么转变成平面波状的振荡斑图, 而且两层介质振荡是反相的, 此外在模拟中还观察到两螺旋波局部间歇锁频现象, 这些结果有助于人们理解在心脏系统中出现的复杂现象.     

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.