论文标题
具有惯性的确定性和随机绞盘模型的相锁状态的出现
Emergence of phase-locked states for a deterministic and stochastic Winfree model with inertia
论文作者
论文摘要
我们研究了惯性作用下无绞膜振荡器的相锁定的出现。众所周知，在大型耦合方案中，由确定性二阶无绞膜模型控制的振荡器，惯性收敛到独特的平衡。相反，在本文中，我们显示了在适当小的耦合方面中非平凡同步的渐近出现。此外，我们研究了具有乘法噪声的新的随机扰动的无绞膜系统的效果，并获得较低的估计性，前提是这种同步模式的路径出现的概率，只要噪声足够小。我们还提供了数值模拟，这些模拟暗示了更一般和更强的分析结果的可能性。
We study the emergence of phase-locking for Winfree oscillators under the effect of inertia. It is known that in a large coupling regime, oscillators governed by the deterministic second-order Winfree model with inertia converge to a unique equilibrium. In contrast, in this paper we show the asymptotic emergence of non-trivial synchronization in a suitably small coupling regime. Moreover, we study the effect of a new stochastically perturbed Winfree system with multiplicative noise and obtain lower estimates in probability for the pathwise emergence of such a synchronizing pattern, provided the noise is sufficiently small. We also provide numerical simulations which hint at the possibility of more general and stronger analytical results.
