Lee Seungjae, Kuklinski Lennart J, Timme Marc
Chair for Network Dynamics, Institute of Theoretical Physics and Center for Advancing Electronics Dresden (cfaed), Technische Universität Dresden, 01062, Dresden, Germany.
Cluster of Excellence Physics of Life, Technische Universität Dresden, 01062, Dresden, Germany.
Nat Commun. 2025 May 15;16(1):4505. doi: 10.1038/s41467-025-59729-8.
Across natural and human-made systems, transition points mark sudden changes of order and are thus key to understanding overarching system features. Motivated by recent experimental observations, we here uncover an intriguing class of transitions in coupled oscillators, extreme synchronization transitions, from asynchronous disordered states to synchronous states with almost completely ordered phases. Whereas such a transition appears like discontinuous or explosive phase transitions, it exhibits markedly distinct features. First, the transition occurs already in finite systems of N units and so constitutes an intriguing bifurcation of multi-dimensional systems rather than a genuine phase transition that emerges in the thermodynamic limit N → ∞ only. Second, the synchronization order parameter jumps from moderate values of the order of N to values extremely close to 1, its theoretical maximum, immediately upon crossing a critical coupling strength. We analytically explain the mechanisms underlying such extreme transitions in coupled complexified Kuramoto oscillators. Extreme transitions may similarly occur across other systems of coupled oscillators as well as in certain percolation processes. In applications, their occurrence impacts our ability of ensuring or preventing strong forms of ordering, for instance in biological and engineered systems.
在自然系统和人造系统中，转变点标志着秩序的突然变化，因此是理解总体系统特征的关键。受近期实验观察结果的启发，我们在此揭示了一类有趣的耦合振子转变，即极端同步转变，从异步无序状态到具有几乎完全有序相位的同步状态。虽然这种转变看起来像不连续或爆发性的相变，但它表现出明显不同的特征。首先，这种转变已经在由N个单元组成的有限系统中发生，因此构成了多维系统中一种有趣的分岔，而不是仅在热力学极限N→∞时才出现的真正相变。其次，同步序参量在越过临界耦合强度时，会立即从N量级的适中值跃升至极其接近1（其理论最大值）的值。我们通过分析解释了耦合的复杂Kuramoto振子中此类极端转变的潜在机制。极端转变同样可能在其他耦合振子系统以及某些渗流过程中出现。在应用中，它们的出现会影响我们确保或防止强形式有序性的能力，例如在生物和工程系统中。
