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.     

传导延迟对螺旋波动力学行为的影响

采用Greenberg-Hastings离散激发介质模型研究传导延迟对螺旋波动力学行为的影响.模拟结果表明:某些情况下,延迟对螺旋波动力学行为无影响;在适当参数下,可观察到螺旋波波长和波速的改变、呼吸螺旋波、多臂螺旋波以及螺旋波和反螺旋波共存现象,对产生这些现象的物理机制作了简要的解释.     

多可激性障碍下的螺旋波动力学

在许多实际可激系统中局部不均匀是广泛存在的, 它们是螺旋波形成以及动力学行为改变的重要因素. 本文研究了可激性障碍对螺旋波动力学行为的影响. 研究表明, 在障碍区域内可激性参数大于区域外情况下障碍会对其附近的螺旋波波头有吸引作用, 多局部障碍共存时吸引行为不仅依赖障碍分布, 而且依赖障碍的大小以及区域内可激性参数的具体取值. 通过抑制变量小值区域的变化分析了这些行为发生的原因. 在障碍区域内可激性参数小于区域外情况下障碍对其近邻的螺旋波波头有排斥作用, 排斥后波头的运动依赖初始螺旋波是刚性旋转的还是漫游的. 多局部障碍共存时排斥作用对螺旋波动力学行为的改变依赖障碍的分布、大小与区域内可激性参数的具体取值以及初始螺旋波的类型. 关键词： 螺旋波 时空混沌 可激性障碍     

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     

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.     

耦合复金兹堡-朗道(Ginzburg-Landau)方程中的模螺旋波

以双层耦合复金兹堡-朗道(Ginzburg-Landau)方程系统为时空模型, 研究了其中的模螺旋波, 讨论了这种特殊波动现象的稳定条件和相关影响因素. 模螺旋波与该类时空系统中常见的相螺旋波相比, 其中心不存在缺陷点, 同时仅在其变量的振幅部分(而非相位部分) 表现为螺旋结构. 本文通过数值方法研究了耦合复金兹堡-朗道方程中产生模螺旋波所需要的初始和参数条件.研究表明, 当双层耦合系统的初始斑图之间的差距较大时, 才能够产生模螺旋波; 同时观察到系统在参数不匹配的条件下会发生相螺旋波向模螺旋波的转变.通过对同步函数的计算, 发现该转变过程具有非连续性.     

随机扰动对螺旋波动力学的影响研究

心脏中的心肌组织是一种典型的可激发介质, 鉴于心肌细胞分布的离散性, 采用离散可激发介质模型研究了不应态时间随机扰动对螺旋波动力学行为的影响, 在扰动随机出现情况下, 螺旋波的稳定性与受扰元胞的数目和扰动幅度有关, 数值计算结果表明: 在适当的条件下, 可以观察到螺旋波漫游、破碎和消失现象, 并简要分析了产生这些现象的机理. 关键词： 螺旋波 激发介质 随机扰动     

激发介质相对不应态对螺旋波动力学行为的影响

采用元胞自动机模型研究激发介质相对不应态对螺旋波动力学行为的影响。数值模拟表明：元胞激发阈值存在一临界区间,该区间的螺旋波周期会突然增加,并存在一最大周期,在合适的系统尺寸和状态数下,螺旋波周期不再受相对不应态的影响而只取决于系统的激发阈值;相对不应态导致螺旋波“Z”型漫游、小范围无规律漫游、花瓣状漫游、锯齿状漫游、风车状漫游等复杂的波头运动。观察到稳定螺旋波、漫游螺旋波和螺旋波消失,并对产生这些现象的机制作简要的解释。     

Lévy噪声与周期力共同驱动下的螺旋波动力学

研究加性Lévy噪声与周期外力对FitzHugh-Nagumo可激系统中螺旋波动力学行为的影响.螺旋波波头的运动随外力周期在一定范围内呈规则变化,该规则变化可用相应的傅立叶谱理解,维持该规则变化的是锁频行为.Lévy噪声序列中包含着小概率的大尺度噪声,螺旋波波头运动改变主要来自于它们的影响,本文指出Lévy噪声对波头运动的影响也依赖于外力周期的取值.在适当的参数取值下,Lévy噪声的存在也能导致螺旋波的消失,这为螺旋波的控制、消除提供了一种方法.分析了系统周期与外力周期的锁定行为,给出了不同噪声强度下的Arnold舌,指出随机共振行为的存在.     

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.     

Drift of Spiral Waves in Complex Ginzburg-Landau Equation

The spontaneous drift of the spiral wave in a finite domain in the complex Ginzburg-Landau equation is investigated numerically. By using the interactions between the spiral wave and its images, we propose a phenomenological theory to explain the observations.     

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.     

Spiral Solutions of the Two-Dimensional Complex Ginzburg-Landau Equation

The multi-order exact solutions of the two-dimensional complex Ginzburg-Landau equation are obtained by making use of the wave-packet theory. In these solutions, the zeroth-order exact solution is a plane wave, the first-order exact solutions are shock waves for the amplitude and spiral waves both between the amplitude and the shift of phase and between the shift of phase and the distance.     

Control of Spiral Waves in an Excitable Medium by Applying Close Loop Feedback Scheme

In this paper, a scheme of close-loop feedback is proposed to induce transition of spiral pattern in the excitable media, which is described with the modified FitzHugh-Nagumo model. The numerical simulation results confirm that the stable rotating spiral wave is removed and the whole media becomes homogeneous when appropriate intensity of feedback is used no matter whether the coupling feedback is imposed on the whole media or the sites in one line in the media.     

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.     

Controlling Chaos with Rectificative Feedback Injections in 2D Coupled Complex Ginzburg-Landau Oscillators

A model of two-dimensional coupled complex Ginzburg-Landau oscillators driven by a rectificative feedbackcontroller is used to study controlling spatiotemporal chaos without gradient force items. By properly selecting the signalinjecting position with considering the maximum gap between signals and targets, and adjusting the control time interval,we have finally obtained the efficient chaos control via numerical simulations.     

Controlling Chaos with Rectificative Feedback Injections in 2D Coupled Complex Ginzburg-Landau Oscillators

A model of two-dimensional coupled complex Ginzburg-Landau oscillators driven by a rectificative feedback controller is used to study controlling spatiotemporal chaos without gradient force items. By properly selecting the signal injecting position with considering the maximum gap between signals and targets, and adjusting the control time interval,we have finally obtained the efficient chaos control via numerical simulations.     

激发介质中去极化对螺旋波动力学影响的数值研究

考虑可激发介质的不应态可以被激发,在Bar模型中引入去极化行为,研究去极化对稳定螺旋波的影响.数值模拟结果显示,适当选择去极化阈值、去极化激发时间,可以使螺旋波漂移、漫游,甚至使螺旋波漫游出系统边界,还可以使系统出现宽臂螺旋波、双臂螺旋波、双峰波、多个螺旋波共存、时空混沌等现象.对产生这些现象的机理进行了分析.     

Stabilization of Pattern in Complex Ginzburg-Landau Equation with Spatial Perturbation Scheme

In this paper, a new scheme of spatial perturbation is proposed to stabilize the pattern in the oscillatory media, which could be described with the complex Ginzburg-Landau equation. The numerical simulation results confirm that the spiral wave, antispiral wave and spatiotemporal chaos in the complex Ginzburg-Landau equation could be suppressed, and the scheme is also discussed with the conservative field theory. Furthermore, the spatiotemporal noise is also introduced into the whole media, it just confirms that it is robust to the spatiotemporal noise.