Mikhaylenko Maria, Ramlow Lukas, Jalan Sarika, Zakharova Anna
Laboratory of Solution Chemistry of Advanced Materials and Technologies, ITMO University, 9 Lomonosova Str., Saint Petersburg 197101, Russian Federation.
Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, Berlin 10623, Germany.
Chaos. 2019 Feb;29(2):023122. doi: 10.1063/1.5057418.
We investigate spatio-temporal patterns occurring in a two-layer multiplex network of oscillatory FitzHugh-Nagumo neurons, where each layer is represented by a nonlocally coupled ring. We show that weak multiplexing, i.e., when the coupling between the layers is smaller than that within the layers, can have a significant impact on the dynamics of the neural network. We develop control strategies based on weak multiplexing and demonstrate how the desired state in one layer can be achieved without manipulating its parameters, but only by adjusting the other layer. We find that for coupling range mismatch, weak multiplexing leads to the appearance of chimera states with different shapes of the mean velocity profile for parameter ranges where they do not exist in isolation. Moreover, we show that introducing a coupling strength mismatch between the layers can suppress chimera states with one incoherent domain (one-headed chimeras) and induce various other regimes such as in-phase synchronization or two-headed chimeras. Interestingly, small intra-layer coupling strength mismatch allows to achieve solitary states throughout the whole network.
我们研究了振荡的菲茨休 - 纳古莫神经元双层多重网络中出现的时空模式，其中每层由一个非局部耦合环表示。我们表明，弱多重性，即层间耦合小于层内耦合时，会对神经网络的动力学产生重大影响。我们基于弱多重性开发了控制策略，并展示了如何在不操纵一层参数的情况下，仅通过调整另一层来实现该层的期望状态。我们发现，对于耦合范围失配，在孤立状态不存在的参数范围内，弱多重性会导致出现具有不同平均速度分布形状的奇异态。此外，我们表明，在层间引入耦合强度失配可以抑制具有一个非相干域的奇异态（单头奇异态），并诱导出诸如同相同步或双头奇异态等各种其他状态。有趣的是，小的层内耦合强度失配能够在整个网络中实现孤立状态。
