We study the nonlinear dynamics of a surprising phenomenon arising in large networks of excitable elements in response to noise: while at low noise, solutions remain in the vicinity of the resting state and large-noise solutions show asynchronous activity, the network displays orderly, perfectly synchronized periodic responses at intermediate levels of noise. This noise-induced synchronization, distinct from classical stochastic resonance, is fundamentally collective in nature. Indeed, we show that, for noise and coupling within specific ranges, an asymmetry in the transition rates between a resting and an excited regime progressively builds up, leading to an increase in the fraction of excited neurons eventually triggering a chain reaction associated with a macroscopic synchronized excursion and a collective return to rest where this process starts afresh, thus yielding the observed periodic synchronized oscillations. We further uncover a novel antiresonance phenomenon in this regime: noise-induced synchronized oscillations disappear when the system is driven by periodic stimulation with frequency within a specific range (high relative to the spontaneous activity). In that antiresonance regime, the system is optimal for measures of information transmission. This observation provides a new hypothesis accounting for the efficiency of high-frequency stimulation therapies, known as deep brain stimulation, in Parkinson’s disease, a neurodegenerative disease characterized by an increased synchronization of brain motor circuits. We further discuss the universality of these phenomena in the class of stochastic networks of excitable elements with specific coupling and illustrate this universality by analyzing various classical models of neuronal networks. Altogether, these results uncover some universal mechanisms supporting a regularizing impact of noise in excitable systems, reveal a novel antiresonance phenomenon in these systems, and propose a new hypothesis for the efficiency of high-frequency stimulation in Parkinson’s disease.

中文翻译：

---

相互作用的兴奋系统中的噪声诱导的同步和反共振：在帕金森氏病的深部脑刺激中的应用。

我们研究了由可激发元素的大型网络响应噪声而产生的令人惊讶的现象的非线性动力学：在低噪声下，解决方案保持在静止状态附近，大噪声解决方案显示异步活动，网络有序，完美地显示在中等噪声水平下同步周期响应。与经典的随机共振不同，这种噪声引起的同步本质上是集体的。实际上，我们表明，对于特定范围内的噪声和耦合，静止和激发态之间的跃迁速率不对称逐渐建立，导致受激神经元比例的增加最终触发与宏观同步偏移相关的连锁反应，并重新开始该过程的静止集体休息，从而产生观察到的周期性同步振荡。我们进一步发现了这种情况下的一种新型反共振现象：当系统受到特定频率范围内的周期性刺激（相对于自发活动的频率较高）驱动时，噪声引起的同步振荡消失。在这种反共振状态下，该系统是信息传输措施的最佳选择。该观察结果提供了一种新的假设，说明了高频刺激疗法在帕金森氏病中被称为深部脑刺激的功效，一种神经退行性疾病，其特征是大脑运动回路的同步性增强。我们将在具有特定耦合的可激发元素随机网络类中进一步讨论这些现象的普遍性，并通过分析神经网络的各种经典模型来说明这种普遍性。总而言之，这些结果揭示了一些可支持噪声对可激发系统进行正则化影响的通用机制，揭示了这些系统中的一种新型反共振现象，并为高频刺激帕金森氏病的效率提出了新的假设。我们将在具有特定耦合的可激发元素随机网络类中进一步讨论这些现象的普遍性，并通过分析神经网络的各种经典模型来说明这种普遍性。总而言之，这些结果揭示了一些可支持噪声对可激发系统进行正则化影响的通用机制，揭示了这些系统中的一种新型反共振现象，并为高频刺激帕金森氏病的效率提出了新的假设。我们将在具有特定耦合的可激发元素随机网络类中进一步讨论这些现象的普遍性，并通过分析神经网络的各种经典模型来说明这种普遍性。总而言之，这些结果揭示了一些可支持噪声对可激发系统进行正则化影响的通用机制，揭示了这些系统中的一种新型反共振现象，并为高频刺激帕金森氏病的效率提出了新的假设。