Vortex coherent structures on arrays of nonlinear oscillators joined by weak links into topologically nontrivial two-dimensional discrete manifolds have been theoretically studied. A circuit of nonlinear electric oscillators coupled by relatively weak capacitances has been considered as a possible physical implementation of such objects. Numerical experiments have shown that a time-monochromatic external force applied to several oscillators leads to the formation of long-lived and nontrivially interacting vortices in the system against the quasistationary background in a wide range of parameters. The dynamics of vortices depends on the method of “coupling” of the opposite sides of a rectangular array by links, which determines the topology of the resulting manifold (torus, Klein bottle, projective plane, Möbius strip, ring, or disk).

中文翻译：

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耦合非线性振荡器系统中的离散涡旋：电模型的数值结果

从理论上研究了非线性振荡器阵列上的涡旋相干结构，该结构由弱链接连接到拓扑上无关紧要的二维离散流形。由相对弱的电容耦合的非线性电振荡器的电路已经被认为是这种对象的可能的物理实现。数值实验表明，在多个参数上，准静态背景下，施加于多个振荡器的时间单色外力会导致系统中长寿命且非平凡相互作用的涡流的形成。旋涡的动力学取决于通过链接“链接”矩形阵列的相对边的方法，该方法确定了所得歧管（托勒斯，克莱因瓶，射影平面，莫比乌斯带，环或圆盘）的拓扑。