Solar flares, email exchanges, and many natural or social systems exhibit bursty dynamics, with periods of intense activity separated by long inactivity. These patterns often follow power- law distributions in inter-event intervals or event rates. Existing models typically capture only one of these features and rely on non-local memory, which complicates analysis and mechanistic interpretation. We introduce a novel self-reinforcing point process whose event rates are governed by local, Markovian nonlinear dynamics and post-event resets. The model generates power-law tails for both inter-event intervals and event rates over a broad range of exponents observed empirically across natural and human phenomena. Compared to non-local models such as Hawkes processes, our approach is mechanistically simpler, highly analytically tractable, and also easier to simulate. We provide methods for model fitting and validation, establishing this framework as a versatile foundation for the study of bursty phenomena.

翻译：太阳耀斑、电子邮件交流以及许多自然或社会系统均表现出阵发性动态，即高强度活动期与长时间静默期交替出现。这些模式通常在事件间隔或事件发生率上遵循幂律分布。现有模型通常仅能捕捉其中一个特征，且依赖于非局部记忆，这使分析和机制解释变得复杂。我们提出了一种新颖的自强化点过程，其事件发生率由局部、马可夫非线性动力学及事件后重置机制控制。该模型能在经验观测到的自然与人类现象指数范围内，为事件间隔和事件发生率同时生成幂律尾部。相较于霍克斯过程等非局部模型，我们的方法机制更简洁、高度可解析处理，且更易于模拟。我们提供了模型拟合与验证方法，确立该框架为研究阵发性现象的通用基础。