The brain is a complex, nonlinear system, exhibiting ever-evolving patterns of activities, whether in the presence or absence of external stimuli or task demands. Nonlinearity can notably obscure the link between structural constraints enforced on the interaction and its dynamical consequences. Suitable nonlinear dynamical models and their analysis serve as essential tools not only for bridging structural and functional understanding of the brain but also for predictably altering the complex dynamical organization of the brain. Here, starting from a large-scale network of threshold Hodgkin–Huxley style neurons, we formulate the average nonlinear dynamics implicitly following from the Wilson–Cowan assumptions. We investigate the influence of biophysical and structural properties on the complexity of neural dynamics at the microscale level and its relationship with the macroscopic Wilson–Cowan model. Incorporating the elements in the model can help identify more realistic regimes of activity and connect the mathematical prediction of increasing nonlinearity to physical manipulations. Our simulations of the temporal profiles reveal dependency on the binary state of interacting subpopulations and the random property of structural network at the transition points, when different synaptic weights are considered. For substantial configurations of stimulus intensity, our model provides further estimates of the neural population’s dynamics, ranging from simple-periodic to aperiodic patterns and phase transition regimes. This reflects the potential contribution of the microscopic nonlinear scheme to the mean-field approximation in studying the collective behaviour of individual neurons with particularly concentrating on the occurrence of critical phenomena. We show that finite-size effects kick the system in a state of irregular modes to evolve differently from predictions of the original Wilson–Cowan reference. Additionally, we report that the complexity and temporal diversity of neural dynamics, especially in terms of limit cycle trajectory, and synchronization can be induced by either small heterogeneity in the degree of various types of local excitatory connectivity or considerable diversity in the external drive to the excitatory pool.

中文翻译：

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神经元的舞蹈：探索大脑网络中的非线性动力学


大脑是一个复杂的非线性系统，无论是否存在外部刺激或任务要求，都会表现出不断演变的活动模式。非线性会明显掩盖相互作用所施加的结构约束与其动态后果之间的联系。合适的非线性动力学模型及其分析不仅可以作为桥接大脑结构和功能理解的重要工具，而且可以作为可预测地改变大脑复杂动态组织的重要工具。在这里，从阈值 Hodgkin-Huxley 型神经元的大规模网络开始，我们隐式地根据 Wilson-Cowan 假设制定了平均非线性动力学。我们研究了生物物理和结构特性对微观层面神经动力学复杂性的影响及其与宏观威尔逊-考恩模型的关系。将元素纳入模型中可以帮助识别更现实的活动机制，并将非线性增加的数学预测与物理操作联系起来。当考虑不同的突触权重时，我们对时间分布的模拟揭示了对相互作用子群的二元状态和过渡点结构网络的随机属性的依赖性。对于刺激强度的实质性配置，我们的模型提供了对神经群体动态的进一步估计，范围从简单周期性到非周期性模式和相变机制。这反映了微观非线性方案对平均场近似在研究单个神经元的集体行为（特别是关注关键现象的发生）方面的潜在贡献。 我们证明，有限尺寸效应会使系统进入不规则模式状态，从而与原始威尔逊-考恩参考文献的预测不同地演化。此外，我们报告说，神经动力学的复杂性和时间多样性，特别是在极限循环轨迹方面，和同步可以由各种类型的局部兴奋连接程度的小异质性或外部驱动的相当大的多样性引起。兴奋池。