Sharma Abhishek, Rajwani Priyanka, Jalan Sarika
Complex Systems Lab, Department of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, India.
Chaos. 2024 Aug 1;34(8). doi: 10.1063/5.0224001.
Coupled oscillators models help us in understanding the origin of synchronization phenomenon prevalent in both natural and artificial systems. Here, we study the coupled Kuramoto oscillator model having phase lag and adaptation in higher-order interactions. We find that the type of transition to synchronization changes from the first-order to second-order through tiered synchronization depending on the adaptation parameters. Phase lag enables this transition at a lower exponent of the adaptation parameters. Moreover, an interplay between the adaptation and phase lag parameters eliminates tiered synchronization, facilitating a direct transition from the first to second-order. In the thermodynamic limit, the Ott-Antonsen approach accurately describes all stationary and (un)stable states, with analytical results matching those obtained from numerical simulations for finite system sizes.
耦合振子模型有助于我们理解自然和人工系统中普遍存在的同步现象的起源。在此，我们研究了在高阶相互作用中具有相位滞后和适应性的耦合Kuramoto振子模型。我们发现，根据适应性参数，通过分层同步，向同步的转变类型从一阶变为二阶。相位滞后使得在适应性参数的较低指数下就能实现这种转变。此外，适应性参数和相位滞后参数之间的相互作用消除了分层同步，促进了从一阶到二阶的直接转变。在热力学极限下，Ott-Antonsen方法准确地描述了所有稳态和（非）稳定状态，解析结果与有限系统规模数值模拟得到的结果相匹配。
