论文标题
量化从螺旋波到螺旋波嵌合体的过渡
Quantifying the transition from spiral waves to spiral wave chimeras in a lattice of self-sustained oscillators
论文作者
论文摘要
目前的工作致力于对具有二维几何形状的自我维持振荡器网络中从螺旋波到螺旋波嵌合体的过渡。网络的基本要素是范德波尔振荡器和Fitzhugh-Nagumo神经元。这两种模型都处于放松振荡方面。我们通过使用局部灵敏度的指标来分析该制度，这使我们能够在有限的时间评估每个单独振荡器的灵敏度。当元素之间的相互作用具有局部特征时，在两个晶格中都可以观察到Spi-ral。所有元素的动态都是规则的。没有高敏感区域。我们发现，当耦合变为非本地时，系统的特征会显着变化。螺旋波中心元件的振荡状态切换到混乱。除此之外，该振荡器周围发生了高灵敏度的区域。此外，我们表明后者随着耦合范围的伸长而在空间中扩展。结果，螺旋波嵌合体的不一致簇正好在此高敏感区域内形成。该群集的形成伴随着最大Lyapunov指数到正区域的值的急剧增加。此外，我们探讨了当几个Lyapunov指数变为正时，系统甚至可以切换到过度循环状态。
The present work is devoted to the detailed quantification of the transition from spiral waves to spiral wave chimeras in a network of self-sustained oscillators with two-dimensional geometry. The basic elements of the networks are the van der Pol oscillator and the FitzHugh-Nagumo neuron. Both models are in the regime of relaxation oscillations. We analyze the regime by using the indices of local sensitivity which enables us to evaluate the sensitivity of each individual oscillator at finite time. Spi-ral waves are observed in both lattices when the interaction between elements have the local character. The dynamics of all the elements is regular. There are no high-sensitive regions. We have discovered that when the coupling becomes nonlocal, the features of the systems significantly changes. The oscillation regime of the spiral wave center element switches to chaotic one. Besides this, a region with high sensitivity occurs around this oscillator. Moreover, we show that the latter expands in space with elongation of the coupling range. As a result, an incoherence cluster of the spiral wave chimera is formed exactly within this high-sensitive area. Formation of this cluster is accompanied by the sharp increase in values of the maximal Lyapunov exponent to the positive region. Furthermore, we explore that the system can even switch to hyperchaotic regime, when several Lyapunov exponents becomes positive.
