Sarkar Mrinal, Gupta Shamik
Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India.
Department of Physics, Ramakrishna Mission Vivekananda Educational and Research Institute, Belur Math, Howrah 711202, India.
Chaos. 2022 Jul;32(7):073109. doi: 10.1063/5.0090861.
What happens when the paradigmatic Kuramoto model involving interacting oscillators of distributed natural frequencies and showing spontaneous collective synchronization in the stationary state is subject to random and repeated interruptions of its dynamics with a reset to the initial condition? While resetting to a synchronized state, it may happen between two successive resets that the system desynchronizes, which depends on the duration of the random time interval between the two resets. Here, we unveil how such a protocol of stochastic resetting dramatically modifies the phase diagram of the bare model, allowing, in particular, for the emergence of a synchronized phase even in parameter regimes for which the bare model does not support such a phase. Our results are based on an exact analysis invoking the celebrated Ott-Antonsen ansatz for the case of the Lorentzian distribution of natural frequencies and numerical results for Gaussian frequency distribution. Our work provides a simple protocol to induce global synchrony in the system through stochastic resetting.
当涉及具有分布自然频率的相互作用振子且在稳态下表现出自发集体同步的典型Kuramoto模型受到其动力学的随机且重复中断并重置到初始条件时会发生什么？在重置到同步状态时，在两次连续重置之间，系统可能会失步，这取决于两次重置之间随机时间间隔的持续时间。在此，我们揭示了这样一种随机重置协议如何显著修改裸模型的相图，特别是允许在裸模型不支持同步相的参数区域中出现同步相。我们的结果基于对自然频率的洛伦兹分布情况调用著名的Ott - Antonsen假设的精确分析以及高斯频率分布的数值结果。我们的工作提供了一种通过随机重置在系统中诱导全局同步的简单协议。
