共查询到20条相似文献,搜索用时 15 毫秒
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A new type of waves in an excitable medium, characterized by oscillatory profile, is described. The excitable medium is modeled by a two-component activator-inhibitor system. Reaction-diffusion systems with diagonal and cross diffusion are examined. As an example, a front (kink) represented by a heteroclinic orbit in the phase space is considered. The wave shape and velocity are analyzed with the use of exact analytical solutions for wave profiles. 相似文献
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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. 相似文献
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Experimental and computational studies of the formation and evolution of scroll waves in three-dimensional excitable media are presented. Scroll waves are initiated in the photosensitive Belousov-Zhabotinsky reaction by perturbing traveling waves transverse to their direction of propagation. Scroll rings are generated by perturbing circular waves, which expand or contract depending on the strength of an imposed excitability gradient and its direction relative to the rotational direction of the scroll wave. (c) 1998 American Institute of Physics. 相似文献
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The selection of shape and rotation frequency for scroll waves in reaction-diffusion equations modeling excitable media is investigated. For scrolls with uniform twist about straight filaments, asymptotic methods are used to derive free-boundary equations at leading and first order. Both orders are validated against full solutions of the reaction-diffusion equations. Using these two orders and with no adjustable parameters, the shape and frequency of waves are correctly predicted except possibly near the point of propagation failure where the core becomes large. 相似文献
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Algebraic formulas predicting the frequencies and shapes of waves in a reaction-diffusion model of excitable media are presented in the form of four recipes. The formulas themselves are based on a detailed asymptotic analysis (published elsewhere) of the model equations at leading order and first order in the asymptotic parameter. The importance of the first order contribution is stressed throughout, beginning with a discussion of the Fife limit, Fife scaling, and Fife regime. Recipes are given for spiral waves and detailed comparisons are presented between the asymptotic predictions and the solutions of the full reaction-diffusion equations. Recipes for twisted scroll waves with straight filaments are given and again comparisons are shown. The connection between the asymptotic results and filament dynamics is discussed, and one of the previously unknown coefficients in the theory of filament dynamics is evaluated in terms of its asymptotic expansion. (c) 2002 American Institute of Physics. 相似文献
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In this paper we calculate the rotation frequency of spiral waves as a function of the parameters of the excitable medium. We give the complete analytical solution in the special case of the Rinzel-Keller model and suggest an analytical procedure for general two-component relaxational reaction-diffusion models. This procedure is based on the Greenberg equation and stability analysis; it is applicable when the core of a spiral wave is large as compared with the characteristic diffusion length. Construction of spiral wave solutions for the waves inside ring channels, circular regions, or around holes is discussed. Multi-armed spiral waves are investigated. 相似文献
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Osipov GV Collins JJ 《Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics》1999,60(1):54-57
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. 相似文献
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采用Br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. 相似文献
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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. 相似文献
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Anchoring of spiral and scroll waves in excitable media has attracted considerable interest in the context of cardiac arrhythmias. Here, by bombarding inclusions with drifting spiral and scroll waves, we explore the forces exerted by inclusions onto an approaching spiral and derive the equations of motion governing spiral dynamics in the vicinity of inclusion. We demonstrate that these forces nonmonotonically depend on distance and can lead to complex behavior: (a)?anchoring to small but circumnavigating larger inclusions; (b)?chirality-dependent anchoring. 相似文献
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Chemical waves are initiated in an excitable medium by resonance with local periodic forcing of the excitability. Experiments are carried out with a photosensitive Belousov-Zhabotinsky medium, in which the excitability is varied according to the intensity of the imposed illumination. Complex resonance patterns are exhibited as a function of the amplitude and frequency of the forcing. Local resonance-induced wave initiation transforms the medium globally from a quiescent excitable steady state to a periodic state of successive traveling waves. 相似文献
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Joseph Starobin Yuri I. Zilberter C.Frank Starmer 《Physica D: Nonlinear Phenomena》1994,70(4):321-341
Potentially life-threatening cardiac arrhythmias can be iniated with stimuli timed to occur during the “vulnerable window (VW)”. We defined VW as the time interval between the “conditioning” and “test” stimuli following in sequence, during which the test stimulus response propagates in only one direction. We show that the VW is a generic feature of excitable media and describe the relationship between the properties of an excitable medium and the VW. We present asymptotic results that reveal the sensitivity of the VW to both the propagation velocity of the conditioning wavefront and the recovery process parameters. We also have identified a critical length of medium that must be excited in order to reveal vulnerability. Analytical results are in agreement with numerical studies. 相似文献
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Universal relationships between the medium excitability and the angular velocity and the core radius of rigidly rotating spiral waves in excitable media are derived for situations where the wave front is a trigger wave and the wave back is a phase wave. Two universal limits restricting the region of existence of spiral waves in the parameter space are demonstrated. The predictions of the free-boundary approach are in good quantitative agreement with results from numerical reaction-diffusion simulations performed on the Kessler-Levine model. 相似文献