受挫振荡网络中出现的不稳定性:分层模块化的关键作用。

Frontiers in network physiology Pub Date : 2024-08-21 eCollection Date: 2024-01-01 DOI:10.3389/fnetp.2024.1436046
Enrico Caprioglio, Luc Berthouze
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引用次数: 0

摘要

可变系统中的振荡复杂网络已被用于研究大脑中综合和分离活动的出现,这些活动被认为是认知的基础。然而,实现可变机制所需的参数和内在机制却很难确定,通常只能依靠最大限度地提高与经验功能连接动态的相关性。在这里,我们提出并证明,大脑的分层模块化中尺度结构本身就能在存在相位挫折的情况下产生稳健的可迁移动力学和(可迁移)嵌合体状态。我们构建了由相同的仓本-坂口振荡器组成的非加权三层分层网络,其参数为网络的平均度和一个结构参数,该参数决定了上两层区块之间和区块内部的连接比例。这些参数共同影响系统的特征时标。在远离临界同步点的地方,我们检测到最底层分层中出现了与上层中的嵌合态和陨落态共存的陨落态。利用拉普拉斯重正化群流方法,我们发现了在这些不同层次中实现可变状态的两种不同途径。在上层,我们展示了对称破缺态如何依赖于系统的慢特征模型。相反,在最底层,当层与层之间的时标分离达到临界阈值时,就可以实现可迁移动力学。我们的研究结果表明,可代谢性、嵌合体状态和系统的特征模型之间存在明确的关系,从而弥补了基于谐波的经验数据研究和振荡模型之间的差距。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Emergence of metastability in frustrated oscillatory networks: the key role of hierarchical modularity.

Oscillatory complex networks in the metastable regime have been used to study the emergence of integrated and segregated activity in the brain, which are hypothesised to be fundamental for cognition. Yet, the parameters and the underlying mechanisms necessary to achieve the metastable regime are hard to identify, often relying on maximising the correlation with empirical functional connectivity dynamics. Here, we propose and show that the brain's hierarchically modular mesoscale structure alone can give rise to robust metastable dynamics and (metastable) chimera states in the presence of phase frustration. We construct unweighted 3-layer hierarchical networks of identical Kuramoto-Sakaguchi oscillators, parameterized by the average degree of the network and a structural parameter determining the ratio of connections between and within blocks in the upper two layers. Together, these parameters affect the characteristic timescales of the system. Away from the critical synchronization point, we detect the emergence of metastable states in the lowest hierarchical layer coexisting with chimera and metastable states in the upper layers. Using the Laplacian renormalization group flow approach, we uncover two distinct pathways towards achieving the metastable regimes detected in these distinct layers. In the upper layers, we show how the symmetry-breaking states depend on the slow eigenmodes of the system. In the lowest layer instead, metastable dynamics can be achieved as the separation of timescales between layers reaches a critical threshold. Our results show an explicit relationship between metastability, chimera states, and the eigenmodes of the system, bridging the gap between harmonic based studies of empirical data and oscillatory models.

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