Rybalova E, Anishchenko V S, Strelkova G I, Zakharova A
Department of Physics, Saratov National Research State University, 83 Astrakhanskaya Street, Saratov 410012, Russia.
Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany.
Chaos. 2019 Jul;29(7):071106. doi: 10.1063/1.5113789.
We investigate solitary states and solitary state chimeras in a ring of nonlocally coupled systems represented by FitzHugh-Nagumo neurons in the oscillatory regime. We perform a systematic study of solitary states in this network. In particular, we explore the phase space structure, calculate basins of attraction, analyze the region of existence of solitary states in the system's parameter space, and investigate how the number of solitary nodes in the network depends on the coupling parameters. We report for the first time the occurrence of solitary state chimera in networks of coupled time-continuous neural systems. Our results disclose distinctive features characteristic of solitary states in the FitzHugh-Nagumo model, such as the flat mean phase velocity profile. On the other hand, we show that the mechanism of solitary states' formation in the FitzHugh-Nagumo model similar to chaotic maps and the Kuramoto model with inertia is related to the appearance of bistability in the system for certain values of coupling parameters. This indicates a general, probably a universal desynchronization scenario via solitary states in networks of very different nature.
我们研究了由处于振荡状态的FitzHugh-Nagumo神经元表示的非局部耦合系统环中的孤立态和孤立态嵌合体。我们对该网络中的孤立态进行了系统研究。具体而言，我们探索了相空间结构，计算了吸引盆，分析了系统参数空间中孤立态的存在区域，并研究了网络中孤立节点的数量如何依赖于耦合参数。我们首次报道了在耦合时间连续神经网络中出现孤立态嵌合体。我们的结果揭示了FitzHugh-Nagumo模型中孤立态的独特特征，例如平坦的平均相速度分布。另一方面，我们表明，FitzHugh-Nagumo模型中类似于具有惯性的混沌映射和Kuramoto模型的孤立态形成机制与系统在某些耦合参数值下出现双稳性有关。这表明了一种通过性质非常不同的网络中的孤立态实现的普遍的、可能是通用的去同步情景。
