AI 中文总结
该研究揭示神经元活动与病理蛋白传播的非线性反馈可在网络传播中产生滞后性与多稳态，其结果或为神经退行性疾病的控制提供新思路。
AI 中文摘要
网络上的传播过程常与同一节点上的其他动态相互作用，神经退行性疾病便是一例：病理蛋白通过解剖连接传播，而神经元活动既会影响其传播，也会被传播改变，形成传播-活动反馈回路。不过，将病理蛋白传播与神经元活动耦合的模型大多聚焦于两者间的线性反馈。本文表明，非线性反馈可从根本上改变易染-感染-易染（SIS）传播过程耦合共进化活动过程的入侵动态。在一般加权网络上，反馈的强度与形状可产生有限振幅入侵阈值、滞后性及地方病多稳态；在具有同质动态的正则图上，排除周期解，且多项式耦合函数的阶数约束地方病状态的数量，而单调耦合需强化反馈才能产生多稳态。我们在由二次发放神经元动态描述的随机脉冲神经元网络模拟中验证了这些预测，成功复现有限振幅入侵阈值与地方病双稳态。这些结果表明，活动过程的反馈可在网络传播动态中产生滞后性与多稳态，在神经科学应用中，本研究提示神经元动态可作为神经退行性疾病的控制点，即使是短暂的活动变化也能使大脑在健康与疾病状态间切换。
英文摘要
Spreading processes on networks often interact with other dynamics on the same nodes. Neurodegenerative disease provides one example: pathological proteins spread through anatomical connections, while neuronal activity influences and is altered by their spread, forming a spreading-activity feedback loop. However, models coupling pathological protein spreading and neuronal activity have largely focused on linear feedback between the two processes. Here we show that nonlinear feedback can fundamentally change the invasion dynamics in a susceptible--infected--susceptible spreading process coupled to a co-evolving activity process. On general weighted networks, the strength and shape of the feedback may generate finite-amplitude invasion thresholds, hysteresis, and endemic multistability. On regular graphs with homogeneous dynamics, we rule out periodic solutions and show that the degrees of polynomial coupling functions bound the number of endemic states, while monotone couplings require reinforcing feedback for multistability. We test these predictions in simulations of a stochastic spiking neuronal network described by quadratic integrate-and-fire dynamics, where we recover both finite-amplitude invasion thresholds and endemic bistability. These results show that feedback from activity processes can create hysteresis and multistability in network spreading dynamics. In neuroscientific applications, our work suggests that neuronal dynamics may act as a control point in neurodegenerative disease, with even transient changes in activity capable of tipping the brain between health and disease.
