Common mechanism links spiral wave meandering and wave-front–obstacle separation
| Autor: | Joseph M. Starobin, C F Starmer |
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| Rok vydání: | 1997 |
| Předmět: | |
| Zdroj: | Physical Review E. 55:1193-1196 |
| ISSN: | 1095-3787 1063-651X |
| DOI: | 10.1103/physreve.55.1193 |
| Popis: | Spiral waves appear in many excitable chemical and biological media @1#. The spiral wave tip either rotates around a circular unexcited core or meanders, inscribing a noncircular pattern often similar to that of a multipetal flower. From numerical studies of FitzHugh-Nagumo-like models for a variety of medium parameters, Zykov @2# and Winfree @3# found a distinct boundary separating meandering from circular tip movement, suggesting that transitions between different modes of tip movement were dependent on certain medium parameter values. The transition from circular spiral tip motion to meandering is known to occur when the spiral tip approaches its refractory tail. The minimal distance between the spiral tip and refractory tail associated with the meandering transition and its relation to medium properties, though, is uncertain. Recently numerical studies of Karma @4# showed that meandering corresponds to the superposition of two rotating spiral wave solutions. He found that the reaction-diffusion field at points located on the wave front near the minimal core radius associated with the meandering transition ~determined numerically! displayed quasiperiodic variations originating from a supercritical Hopf bifurcation. Analytical investigations of spiral core stability by Kessler et al. @5# based on kinematic theory did not confirm this behavior, probably because their analysis was performed within a kinematic framework that differed significantly from the framework of Karma’s analysis @4#. Moreover, the kinematic approach is limited by the assumption that the wave radius of curvature is large compared with the wavelength, a condition that is not fulfilled at the spiral tip @6#. Barkley developed a phenomenological model that reproduced complex spiral tip movement @7#. However, based on the ordinary differential equation representation, this model did not describe the transition to meandering and did not provide a minimal core radius associated with a meandering transition boundary since it neglected generic diffusive properties of an excitable medium. In this paper, we show that the conditions associated with the meandering transition are equivalent to conditions associated with the transition between wave-front‐obstacle attachment and separation following a wave-obstacle interaction @Fig. 1~a!#. We found that the minimal distance that the spiral wave tip can approach its refractory tail without meandering is of the order of Lcrit , the wave-front thickness of a wave propagating with zero velocity. Following interaction with an unexcitable strip of thickness Lcrit , there are two possible outcomes. If the wave tip wraps itself around the end of this unexcitable strip, then it will meander if the strip is removed. Alternatively, if the wave tip separates from the end of the strip, then removal will result in circular spiral tip motion. Over a range of medium parameters, this transition can be accurately predicted by approximating the diffusive fluxes within the boundary layer at the wave tip @9,10#. Here we consider nonlinear reaction-diffusion equations of the FitzHugh-Nagumo class |
| Databáze: | OpenAIRE |
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