Yadav Akash, Fialkowski Jan, Berner Rico, Chandrasekar V K, Senthilkumar D V
School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram-695551, Kerala, India.
Complexity Science Hub Vienna, Josefstädter Straße 39, 1080 Vienna, Austria.
Phys Rev E. 2024 May;109(5):L052301. doi: 10.1103/PhysRevE.109.L052301.
Phase transitions are crucial in shaping the collective dynamics of a broad spectrum of natural systems across disciplines. Here, we report two distinct heterogeneous nucleation facilitating single step and multistep phase transitions to global synchronization in a finite-size adaptive network due to the trade off between time scale adaptation and coupling strength disparities. Specifically, small intracluster nucleations coalesce either at the population interface or within the populations resulting in the two distinct phase transitions depending on the degree of the disparities. We find that the coupling strength disparity largely controls the nature of phase transition in the phase diagram irrespective of the adaptation disparity. We provide a mesoscopic description for the cluster dynamics using the collective coordinates approach that brilliantly captures the multicluster dynamics among the populations leading to distinct phase transitions. Further, we also deduce the upper bound for the coupling strength for the existence of two intraclusters explicitly in terms of adaptation and coupling strength disparities. These insights may have implications across domains ranging from neurological disorders to segregation dynamics in social networks.
相变在塑造跨学科的广泛自然系统的集体动力学方面至关重要。在此，我们报告了两种不同的异质成核现象，由于时间尺度适应和耦合强度差异之间的权衡，它们促进了有限规模自适应网络中的单步和多步相变至全局同步。具体而言，小的簇内成核在种群界面处或种群内部合并，根据差异程度导致两种不同的相变。我们发现，耦合强度差异在很大程度上控制了相图中相变的性质，而与适应差异无关。我们使用集体坐标方法对簇动力学进行了介观描述，该方法出色地捕捉了种群之间导致不同相变的多簇动力学。此外，我们还根据适应和耦合强度差异明确推导出了两个簇内存在时耦合强度的上限。这些见解可能对从神经疾病到社交网络中的隔离动力学等各个领域都有影响。
