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.     

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

The influence of long-range links on spiral waves in excitable medium has been investigated. Spatiotemporal dynamics in excitable small-world network transforms 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 control spiral wave and spiral turbulence successfully.     

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.     

Stimulus-induced response patterns of medium-embedded neurons

Neuronal ensembles in living organisms are often embedded in a media that provides additional interaction pathways and autoregulation. The underlying mechanisms include but are not limited to modulatory activity of some distantly propagated neuromediators like serotonin, variation of extracellular potassium concentration in brain tissue, and calcium waves propagation in networks of astrocytes. Interaction of these diverse processes can lead to formation of complex spatiotemporal patterns, both self-sustained or triggered by external signal. Besides network effects, many dynamical features of such systems originate from reciprocal interaction between single neuron and surrounding medium. In the present paper we study the response of such systems to the application of a single stimulus pulse. We use a minimal mathematical model representing a forced excitable unit that is embedded in a diffusive or (spatially inhomogeneous) excitable medium. We illustrate three different mechanisms for the formation of response patterns: (i) self-sustained depolarization, (ii) propagation of depolarization due to “nearest-neighbor” networks, and (iii) re-entrant waves.     

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.     

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.     

Excitable optical waves in semiconductor microcavities

We demonstrate experimentally and theoretically the existence of excitable optical waves in semiconductor microcavities. Although similar to those observed in biological and chemical systems, these excitable optical waves are self-confined. This is due to a new dynamical scenario, where a stationary Turning pattern controls the propagation of waves in an excitable medium, thus bringing together the two paradigms of dynamical behavior (waves and patterns) in active media.     

Using weak impulses to suppress traveling waves in excitable media

Here we propose mechanisms for suppressing non-steady-state motions--propagating pulses, spiral waves, spiral-wave chaos--in excitable media. Our approach is based on two points: (1) excitable media are multistable; and (2) traveling waves in excitable media can be separated into fast and slow motions, which can be considered independently. We show that weak impulses can be used to change the values of the slow variable at the front and back of a traveling wave, which leads to wave front and wave back velocities that are different from each other. This effect can destabilize the traveling wave, resulting in a transition to the rest state.     

Mechanism of standing wave patterns in cardiac muscle

Recent experiments [R. A. Gray, Phys. Rev. Lett. 87, 168104 (2001)]] have revealed striking standing wave patterns in cardiac muscle. In excitable media, such as cardiac tissue where colliding waves annihilate, standing wave patterns result from a fully nonlinear mechanism. We present a possible physical mechanism explaining these patterns. The phenomenon does not depend on the precise excitable model chosen. Analogies are drawn with weak links in superconductors, and phase-slip solutions in the Ginzburg-Landau equations.     

Stochastic Signal Induced Multiple Spatial Coherence Resonances and Spiral Waves in Excitable Media

Multiple spatial coherence resonances and spiral waves with various temporal-spatial structures are simulated in a two-dimensional network of excitable cells driven by a stochastic signal. The relationship between the multiple resonances and correspondingly different transitions of the spiral wave are elucidated. The results further provide a possible approach of applications of stochastic signal to evoke pattern transitions in excitable media.     

Involutes: the geometry of chemical waves rotating in annular membranes

According to earlier theories certain parts of a chemical wave front propagating in a 2-D excitable medium with a convex obstacle should be involutes of that obstacle. The present paper discusses a special case where self-sustained chemical waves are rotating around a central obstacle in an annular 2-D excitable region. A simple geometrical model of wave propagation based on the Fermat principle (minimum propagation time) is suggested. Applying this model it is shown that the wave fronts in the case of an annular excitable region should be purely involutes of the central obstacle in the asymptotic state. This theory is supported by experiments in a novel membrane reactor where a catalyst of the Belousov-Zhabotinsky reaction is fixed on a porous membrane combined with a gel medium. Involutes of circular and triangular obstacles are observed experimentally. Deviations from the ideal involute geometry are explained by inhomogeneities in the membrane. (c) 1995 American Institute of Physics.     

Nonlinear dynamics of self-sustained supersonic reaction waves: Fickett's detonation analogue

The present study investigates the spatiotemporal variability in the dynamics of self-sustained supersonic reaction waves propagating through an excitable medium. The model is an extension of Fickett's detonation model with a state-dependent energy addition term. Stable and pulsating supersonic waves are predicted. With increasing sensitivity of the reaction rate, the reaction wave transits from steady propagation to stable limit cycles and eventually to chaos through the classical Feigenbaum route. The physical pulsation mechanism is explained by the coherence between internal wave motion and energy release. The results obtained clarify the physical origin of detonation wave instability in chemical detonations previously observed experimentally.     

Varieties of spiral wave behavior: An experimentalist's approach to the theory of excitable media

Spiral waves in diverse excitable media exhibit strikingly variegated behavior. Mechanistic interpretations of excitability in laboratory systems are commonly tested by comparing the wavelength, period, and meander patterns of the model's spiral waves with laboratory observations, but models seem seldom to be rejected by such tests. The reason may be that almost any excitable medium behaves in many respects like almost any other, if its parameters are properly adjusted within a reasonable range. What generalizations can be made about "excitable media" in the absence of more specifications? It would be useful to distinguish such generic features from idiosyncrasies of specific models. The range of behavioral flexibility of the FitzHugh-Nagumo excitable medium is explored by varying two of its parameters and comparing the results with other excitable media to suggest a generic pattern of parameter dependence. The results exhibit the remarkable diversity of rotor behavior in a single model and provide a database for quantitative testing of mathematical generalizations.     

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.     

Suppressing arrhythmias in cardiac models using overdrive pacing and calcium channel blockers

Recent findings indicate that ventricular fibrillation might arise from spiral wave chaos. Our objective in this computational study was to investigate wave interactions in excitable media and to explore the feasibility of using overdrive pacing to suppress spiral wave chaos. This work is based on the finding that in excitable media, propagating waves with the highest excitation frequency eventually overtake all other waves. We analyzed the effects of low-amplitude, high-frequency pacing in one-dimensional and two-dimensional networks of coupled, excitable cells governed by the Luo-Rudy model. In the one-dimensional cardiac model, we found narrow high-frequency regions of 1:1 synchronization between the input stimulus and the system's response. The frequencies in this region were higher than the intrinsic spiral wave frequency of cardiac tissue. When we paced the two-dimensional cardiac model with frequencies from this region, we found that spiral wave chaos could, in some cases, be suppressed. When we coupled the overdrive pacing with calcium channel blockers, we found that spiral wave chaos could be suppressed in all cases. These findings suggest that low-amplitude, high-frequency overdrive pacing, in combination with calcium channel inhibitors (e.g., class II or class IV antiarrhythmic drugs), may be useful for eliminating fibrillation. (c) 2002 American Institute of Physics.     

Transverse coupling of chemical waves

The transverse coupling of chemical waves is investigated using a model scheme for excitable media. Chemical waves supported on the surfaces of a semipermeable membrane couple via diffusion through the membrane, resulting in new types of spatiotemporal behavior. The model studies show that spontaneous wave sources may develop from interacting planar waves, giving rise to a complex sequence of patterns accessible only by perturbation. Coupled circular waves result in the spontaneous formation of spiral waves, which subsequently develop patterns in distinct domains with characteristic features. The long time entrainment behavior of coupled spiral waves reveals regions of 1:2 phase locking.     

Combining spiral and target wave detection to analyze excitable media dynamics

Excitable media dynamics is the lossless active transmission of waves of excitation over a field of coupled elements, such as electrical excitation in heart tissue or nerve fibers, cAMP signaling in the slime mold Dictyostelium discoideum or waves of chemical activity in the Belousov-Zhabotinsky reaction. All these systems follow essentially the same generic dynamics, including undamped wave transmission and the self-organized emergence of circular target and self-sustaining spiral waves. We combine spiral recognition, using the established phase singularity technique, and a novel three-dimensional fitting algorithm for noise-resistant target wave recognition to extract all important events responsible for the layout of the asymptotic large-scale pattern. Space-time plots of these combined events reveal signatures of events leading to spiral formation, illuminating the microscopic mechanisms at work. This strategy can be applied to arbitrary excitable media data from either models or experiments, giving insight into for example the microscopic causes for formation of pathological spiral waves in heart tissue, which could lead to novel techniques for diagnosis, risk evaluation and treatment.     

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     

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.