Collective Dynamics of Deterministic and Noisy Oscillator Populations: Beyond Ott-Antonsen Theory

确定性和噪声振荡器总体的集体动力学：超越奥特-安东森理论

• 批准号: 405856192
• 负责人: Professor Dr. Arkady Pikovsky
• 金额: --
• 依托单位: Institut für Physik und Astronomie
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/405856192?language=en
• 关键词: Collective; Dynamics; Deterministic; Noisy; Oscillator

Synchronization in ensembles of oscillators manifests itself as appearance of a macroscopic collective mode. In a particular situation, such a mode can be described analytically by virtue of the Ott-Antonsen approach. Our first aim in this project is to generalise this approach by constructing an effective perturbation theory near the Ott-Antonsen manifold, thus extending it to non-ideal situations. We will explore with this theory the effects which are not covered by the Ott-Antonsen equations: effects of intrinsic noise, of deterministic high-harmonics perturbations, of disorder in parameters. Our second goal is to study effects of common noise on the synchronization properties of coupled oscillators. The main attention will be devoted to situations where coupling is desynchronizing and thus competes with synchronizing action of noise. While analytical theory will be developed for simplest setups, the effects will be also tested on practically relevant systems like Josephson junctions and spin-torque oscillators.

振子系综的同步表现为宏观集体模的出现。在特定的情况下，这种模式可以分析描述凭借的Escherich-Antonsen方法。我们在该项目中的首要目标是通过在Ott-Antonsen流形附近构建有效的扰动理论来概括这种方法，从而将其扩展到非理想情况。我们将用这个理论来探讨那些没有被K-Antonsen方程所涵盖的效应：固有噪声的效应、确定性高次谐波扰动的效应、参数无序的效应。我们的第二个目标是研究公共噪声对耦合振子同步特性的影响。主要的注意力将致力于耦合的情况下，是desperizing，从而竞争与同步行动的噪音。虽然将为最简单的设置开发分析理论，但也将在约瑟夫森结和自旋扭矩振荡器等实际相关系统上测试其效果。