This study explores the interaction between two distinct sites, termed the source and the sink, to analyze the possibility of spiral wave formation. To this aim, a grid of memristive FitzHugh–Nagumo elements is designed to simulate biological excitable media, such as the myocardium. The source, characterized by high excitation levels with a gradual increase in the recovery variable, is primed to generate an excitatory wavefront. In contrast, the sink remains quiescent in excitation yet elevated in the recovery state, thus tending to absorb excitation as it is temporarily unexcitable but soon recoverable. Existing literature on spiral wave formation primarily focuses on rotor formation under source–sink adjacency. This work, on the other hand, examines the potential for re-entrant behavior under spatial separation between the source and the sink. Within the context of eight-nearest neighbor coupling, the results indicate that the time delay for the excitation wave to reach the refractory state of the sink, due to the increased distance, may still facilitate re-entry if the intensity of connections is sufficiently weak. However, beyond a certain threshold of the source–sink distance under weak connections, wave breakage may occur without resulting in re-entry. For the birth of a spiral wave rotor, the tip of the excitatory wavefront must converge with its refractory back, specifically at the outermost contour in the final stage of refractoriness, referred to as the wavetail. The formation of a spiral rotor cannot arise from a wavefront encountering any site earlier in the stage of refractoriness.

中文翻译：

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弱突触连接可能促进源-库相互作用下螺旋波的形成


这项研究探讨了两个不同地点（称为源和汇）之间的相互作用，以分析螺旋波形成的可能性。为此，设计了忆阻 FitzHugh-Nagumo 元件网格来模拟生物可兴奋介质，例如心肌。该源的特点是高激发水平，恢复变量逐渐增加，准备产生激发波前。相反，接收器在激发状态下保持静止，但在恢复状态下升高，因此倾向于吸收激发，因为它暂时不可激发但很快就会恢复。现有关于螺旋波形成的文献主要集中在源汇邻近情况下的转子形成。另一方面，这项工作研究了源和汇之间的空间分离下重入行为的可能性。在八最近邻耦合的情况下，结果表明，如果连接强度足够弱，由于距离增加，激励波到达汇的难熔状态的时间延迟仍然可能促进重新进入。然而，在弱连接下，超过源-汇距离的某个阈值时，可能会发生波破碎而不会导致重新进入。为了诞生螺旋波转子，兴奋波前的尖端必须与其不应期背部会聚，特别是在不应期最后阶段的最外轮廓处，称为波尾。螺旋转子的形成不能由波前在不应期阶段早期遇到任何位置而产生。