Mehrabbeik Mahtab, Jafari Sajad, Perc Matjaž
Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran.
Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran.
Front Comput Neurosci. 2023 Aug 31;17:1248976. doi: 10.3389/fncom.2023.1248976. eCollection 2023.
Simplicial complexes are mathematical constructions that describe higher-order interactions within the interconnecting elements of a network. Such higher-order interactions become increasingly significant in neuronal networks since biological backgrounds and previous outcomes back them. In light of this, the current research explores a higher-order network of the memristive Rulkov model. To that end, the master stability functions are used to evaluate the synchronization of a network with pure pairwise hybrid (electrical and chemical) synapses alongside a network with two-node electrical and multi-node chemical connections. The findings provide good insight into the impact of incorporating higher-order interaction in a network. Compared to two-node chemical synapses, higher-order interactions adjust the synchronization patterns to lower multi-node chemical coupling parameter values. Furthermore, the effect of altering higher-order coupling parameter value on the dynamics of neurons in the synchronization state is researched. It is also shown how increasing network size can enhance synchronization by lowering the value of coupling parameters whereby synchronization occurs. Except for complete synchronization, cluster synchronization is detected for higher electrical coupling strength values wherein the neurons are out of the completed synchronization state.
单纯复形是一种数学结构，用于描述网络中相互连接元素之间的高阶相互作用。由于生物学背景和先前的研究结果支持，这种高阶相互作用在神经网络中变得越来越重要。有鉴于此，当前的研究探索了忆阻型鲁尔科夫模型的高阶网络。为此，主稳定性函数被用于评估一个具有纯成对混合（电和化学）突触的网络以及一个具有双节点电连接和多节点化学连接的网络的同步情况。这些发现为在网络中纳入高阶相互作用的影响提供了很好的见解。与双节点化学突触相比，高阶相互作用将同步模式调整到更低的多节点化学耦合参数值。此外，还研究了改变高阶耦合参数值对处于同步状态的神经元动力学的影响。研究还表明，增加网络规模如何通过降低发生同步的耦合参数值来增强同步。除了完全同步外，对于较高的电耦合强度值，还检测到了簇同步，其中神经元处于完全同步状态之外。
