Methods that distinguish dynamical regimes in networks of active elements make it possible to design the dynamics of models of realistic networks. A particularly salient example is partial synchronization, which may play a pivotal role in elucidating the dynamics of biological neural networks. Such emergent partial synchronization in structurally homogeneous networks is commonly denoted as chimera states. While several methods for detecting chimeras in networks of spiking neurons have been proposed, these are less effective when applied to networks of bursting neurons. Here we introduce the correlation dimension as a novel approach to identifying dynamic network states. To assess the viability of this new method, we study a network of intrinsically Hindmarsh-Rose neurons with non-local connections. In comparison to other measures of chimera states, the correlation dimension effectively characterizes chimeras in burst neurons, whether the incoherence arises in spikes or bursts. The generality of dimensionality measures inherent in the correlation dimension renders this approach applicable to any dynamic system, facilitating the comparison of simulated and experimental data. We anticipate that this methodology will enable the tuning and simulation of when modelling intricate network processes, contributing to a deeper understanding of neural dynamics.

翻译：区分活性元素网络中动力学状态的方法使得设计现实网络模型的动力学成为可能。一个特别突出的例子是部分同步化，它可能在阐明生物神经网络动力学中发挥关键作用。这种在结构均匀网络中涌现的部分同步化通常被称为嵌合态。尽管已有多种检测脉冲神经元网络中嵌合态的方法被提出，但这些方法在应用于爆发神经元网络时效果较差。本文引入关联维度作为一种识别动态网络状态的新方法。为评估该新方法的可行性，我们研究了一个具有非局部连接的内在Hindmarsh-Rose神经元网络。与其他嵌合态度量相比，关联维度能有效表征爆发神经元中的嵌合态，无论非相干性源自脉冲还是爆发。关联维度中固有的维度度量的普适性使得该方法适用于任何动态系统，从而促进模拟数据与实验数据的比较。我们预期该方法将能够在建模复杂网络过程时实现调谐与模拟，有助于更深入地理解神经动力学。