Influence of Control Parameters on the Competition Between Spiral Waves and Target Waves

In this paper we systematically investigate the influence of control parameters on the competition results between spiral waves and target waves. Driving frequency f, amplitude A and injection area n of the input signals are three important parameters and the competition results between spiral waves and target waves are influenced by these three parameters remarkably. Based on these understandings we can control spiral waves effectively by suitable combination these parameters to generate faster target waves. And the effective controllable parameter regions are also studied.     

Elimination of Anti-spiral Waves by Local Inhomogeneity in Oscillatory Systems

采用系统中的局部不均匀性消除振荡系统中的反螺旋波. 该不均匀性在系统中成为一个波源,不断产生稳定的相波. 研究结果发现,不均匀性的尺寸大小存在一个临界值,如果低于此临界值,则系统将无法激发任何相波. 根据不均匀性形状的不同,系统分别产生靶波和行波. 此外,实验还发现靶波与反螺旋波之间以及行波与反螺旋波之间存在着不同的动态竞争. 数值计算表明,对于行波,无论是低频行波还是高频行波,都可以成功地消除系统中的反螺旋波;而对于靶波,只有低频靶波才可以消除反螺旋波. 此控制方法简单易行,且同样适用于消除向外传播的螺旋波     

复Ginzburg-Landau方程中模螺旋波的稳定性研究

研究了复Ginzburg-Landau方程系统中模螺旋波与其他斑图在同一平面内的竞争行为,发现演化结果在系统参数平面内可分为四个主要区域:在I区和III区中,模螺旋波与相螺旋波相比稳定性较差,模螺旋波的空间被相螺旋波所入侵.在II区中,模螺旋波具有较强的稳定性,相螺旋波的空间被模螺旋波所入侵.在IV区内,由于时空混沌所导致的频率不稳定性,演化的结果较为复杂.我们通过对模螺旋波、相螺旋波以及时空混沌的频率分析,发现当模螺旋波的系统参数为α1=-1.34,β1=0.35时,较高频率的模螺旋波具有较好的稳定性,高频模螺旋波可以入侵低频斑图空间.竞争结果主要受系统变量实部的频率影响,频率分析所得到的理论结果与数值实验结果符合得非常好.     

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.     

Controlling spiral wave with target wave in oscillatory systems

Spiral waves have been controlled by generating target waves with a localized inhomogeneity in the oscillatory medium. The competition between the spiral waves and target waves is discussed. The effect of the localized inhomogeneity size has also been studied.     

局部不均匀性对时空系统振荡频率的影响

以复金兹堡一朗道方程为模型,利用数值实验方法观察了时空系统中螺旋波斑图的演化行为,发现在局域非均匀参数条件下,系统的螺旋波可以受到该杂质区域的影响而演化成为稳定的靶波.研究表明,内传的螺旋波转换为稳定靶波的必要条件是非杂质系统和杂质系统的振荡频率相等且小于系统的固有频率,并在参数一频率空间形成一个特殊的V形区域,进一步分析表明,该V形区域具有左右对称、两侧靶波传播方向相反以及随杂质区域参数α_2的增大而向参数β_2减小方向平移等性质.     

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.     

Meandering Spiral Waves Induced by Time-Periodic Coupling Strength

Effects of time-periodic coupling strength (TPCS) on spiral waves dynamics are studied by numerical computations and mathematical analyses. We find that meandering or drifting spirals waves, which are not observed for the case of constant coupling strength, can be induced by TPCS. In particular, a transition between outward petal and inward petal meandering spirals is observed when the period of TPCS is varied. These two types of meandering spirals are separated by a drifting spiral, which can be induced by TPCS when the period of TPCS is very close to that of rigidly rotating spiral. Similar results can be obtained if the coupling strength is modulated by a rectangle wave. Furthermore, a kinetic model for spiral movement suggested by Di et al., [Phys. Rev. E 85 (2012) 046216] is applied for explaining the above findings. The theoretical results are in good qualitative agreement with numerical simulations.     

Meandering Spiral Waves Induced by Time-Periodic Coupling Strength

Effects of time-periodic coupling strength （TPCS） on spiral waves dynamics are studied by numerical computations and mathematical analyses. We find that meandering or drifting spirals waves, which are not observed for the case of constant coupling strength, can be induced by TPCS. In particular, a transition between outward petal and inward petal meandering spirals is observed when the period of TPCS is varied. These two types of meandering spirals are separated by a drifting spiral, which can be induced by TPCS when the period of TPCS is very close to that of rigidly rotating spiral. Similar results can be obtained if the coupling strength is modulated by a rectangle wave. Furthermore, a kinetic model for spiral movement suggested by Diet al., [Phys. Rev. E 85 （2012） 046216] is applied for explaining the above findings. The theoretical results are in good qualitative agreement with numerical simulations.     

Evolution of Spiral Waves in Excitable Systems

Spiral waves, whose rotation center can be regarded as a point defect, widely exist in various two-dimensional excitable systems. In this paper, by making use of Duan＇s topological current theory, we obtain the charge density of spiral waves and the topological inner structure of its topological charge. The evolution of spiral wave is also studied from the topological properties of a two-dimensional vector field. The spiral waves are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of the two-dimensional vector field. Some applications of our theory are also discussed.     

Phenomenological theory of phase diagrams. The case of Landau’s potentials with \mathcal{L} = 43m

Diversity-induced resonance, the emergence of coherent spatiotemporal patterns at intermediate parameter disorder, is a well-known phenomenon in lattices of excitable elements. Here we study the pattern events behind diversity-induced resonance in a lattice of coupled FitzHugh-Nagumo oscillators. Starting out with the observation that maximal spiral wave counts occur at intermediate values of parameter diversity, we analyze the competition between spiral and target wave patterns in the asymptotic collective state. We devise stylized numerical “in silico” competition experiments of (individual) patterns to understand the regulating parameters of the competing pattern events occurring stochastically in the full (“in vivo”) numerical simulation. Our analysis shows that pattern competition is a principal driving mechanism behind this form of diversity-induced resonance and that different types of competition take place: some follow the frequency composition of target and spiral waves, others are dictated by the statistics of parameter distributions. In particular, the increase and decrease of spiral wave counts with increasing diversity are statistically regulated by the number of oscillatory elements in the lattice, rather than by the frequency differences between target and spiral waves.     

随机相位扰动抑制激发介质中漂移的螺旋波

研究了一类二维变量描述的激发系统中漂移螺旋波的抑制问题.通过在整个系统中局部注入带随机相位的电信号，如在系统256×256格点的边界或中心区域中选取4×4或者5×5格点区域施加一个带随机相位的外部激励电信号，在系统内部产生一个持续的靶波信号，实现靶波对螺旋波的动态竞争.数值计算表明：该方法对于Barkley模型中螺旋波有很强的抑制作用，与简单的局部周期信号驱动比较，具有暂态过程比较短的特点，而且对于时空噪声具有一定的抗干扰性.在一定的噪声范围内，即使系统出现不均匀性，也可以观测到靶波，新出现的靶波对螺旋波有抑制作用. 关键词： 螺旋波 靶波 Barkley模型 随机相位     

Parameter Diversity Induced Multiple Spatial Coherence Resonances and Spiral Waves in Neuronal Network with and Without Noise

Diversity in the neurons and noise are inevitable in the real neuronal network. In this paper, parameter diversity induced spiral waves and multiple spatial coherence resonances in a two-dimensional neuronal network without or with noise are simulated. The relationship between the multiple resonances and the multiple transitions between patterns of spiral waves are identified. The coherence degrees induced by the diversity are suppressed when noise is introduced and noise density is increased. The results suggest that natural nervous system might profit from both parameter diversity and noise, provided a possible approach to control formation and transition of spiral wave by the cooperation between the diversity and noise.     

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。     

B-Z反应中斑图的数值模拟及实验研究

根据B-Z反应的FKN机理得出的二维Tyson模型,用差分方法模拟了靶型波、单螺旋波、双螺旋波的形成过程.通过数值模拟发现螺旋波的组织中心是一个点缺陷,系统所有的动力学行为都受这个缺陷点的影响.在此基础上,在封闭的溴酸盐/硫酸/试亚铁灵的B-Z反应体系中,通过割断靶型波的方法,产生了双螺旋波.同时,也观察到了单螺旋波与螺旋波的破碎.这些实验结果与数值模拟结果一致.将B-Z振荡反应实验引入非线性物理实验教学中,可以扩充时空动力学的实验内容.     

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     

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.     

通过控制钙和钾离子流抑制心脏中的螺旋波和时空混沌

采用LuoRudy91心脏模型研究螺旋波和时空混沌的控制,提出联合使用钙通道激动剂和钾通道阻滞剂的控制策略来增大钙离子电导率和减小钾离子电导率,达到消除心脏组织中的螺旋波和时空混沌的目的.数值模拟结果表明,该方法可以有效抑制螺旋波和时空混沌,即使介质存在无扩散功能的缺陷时该方法仍有效.对控制机制做简单探讨.     

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.     

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.