Abstract：
Dynamical systems on networks typically involve several dynamical processes evolving at different timescales. For instance, in Alzheimer\'s disease, the spread of toxic protein throughout the brain not only disrupts neuronal activity but is also influenced by neuronal activity itself, establishing a feedback loop between the fast neuronal activity and the slow protein spreading. Motivated by the case of Alzheimer\'s disease, we study the multiple-timescale dynamics of a heterodimer spreading process on an adaptive network of Kuramoto oscillators. Using a minimal two-node model, we establish that heterogeneous oscillatory activity facilitates toxic outbreaks and induces symmetry breaking in the spreading patterns. We then extend the model formulation to larger networks and perform numerical simulations of the slow-fast dynamics on common network motifs and on the brain connectome. The simulations corroborate the findings from the minimal model, underscoring the significance of multiple-timescale dynamics in the modeling of neurodegenerative diseases.
摘要：
网络上的动态系统通常涉及在不同时间尺度上演化的几个动态过程。例如,在阿尔茨海默病中，有毒蛋白质在整个大脑中的传播不仅破坏了神经元的活动，而且还受到神经元活动本身的影响，在快速神经元活动和缓慢蛋白质扩散之间建立反馈回路。受阿尔茨海默病的影响，我们在Kuramoto振荡器的自适应网络上研究了异二聚体扩散过程的多时间尺度动力学。使用最小两节点模型，我们确定，异质振荡活动促进了有毒物质的爆发，并引起了传播模式的对称性破坏。然后，我们将模型公式扩展到更大的网络，并对常见网络基序和大脑连接体上的慢速动力学进行数值模拟。模拟证实了最小模型的发现，强调多时间尺度动力学在神经退行性疾病建模中的重要性。
