Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108, India.
Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia.
Sci Rep. 2016 Dec 13;6:39033. doi: 10.1038/srep39033.
Spatial coexistence of coherent and incoherent dynamics in network of coupled oscillators is called a chimera state. We study such chimera states in a network of neurons without any direct interactions but connected through another medium of neurons, forming a multilayer structure. The upper layer is thus made up of uncoupled neurons and the lower layer plays the role of a medium through which the neurons in the upper layer share information among each other. Hindmarsh-Rose neurons with square wave bursting dynamics are considered as nodes in both layers. In addition, we also discuss the existence of chimera states in presence of inter layer heterogeneity. The neurons in the bottom layer are globally connected through electrical synapses, while across the two layers chemical synapses are formed. According to our research, the competing effects of these two types of synapses can lead to chimera states in the upper layer of uncoupled neurons. Remarkably, we find a density-dependent threshold for the emergence of chimera states in uncoupled neurons, similar to the quorum sensing transition to a synchronized state. Finally, we examine the impact of both homogeneous and heterogeneous inter-layer information transmission delays on the observed chimera states over a wide parameter space.
在耦合振荡器网络中，相干和非相干动力学的空间共存称为嵌同态。我们研究了无直接相互作用但通过神经元的另一种介质连接的神经元网络中的这种嵌同态，形成了一种多层结构。上层由非耦合神经元组成，而下层则充当神经元之间相互共享信息的介质。具有方波爆发动力学的 Hindmarsh-Rose 神经元被视为上下两层的节点。此外，我们还讨论了存在层间异质性时嵌同态的存在。底层神经元通过电突触全局连接，而在两层之间形成化学突触。根据我们的研究，这两种类型突触的竞争效应可能导致非耦合神经元上层出现嵌同态。值得注意的是，我们发现非耦合神经元中嵌同态出现的密度相关阈值与群体感应同步到同步状态的转变相似。最后，我们在广泛的参数空间中研究了同层和异层层间信息传输延迟对观察到的嵌同态的影响。
