Yadav Akash, Kar Rumi, Chandrasekar V K, Senthilkumar D V
Indian Institute of Science Education and Research, School of Physics, Thiruvananthapuram-695551, Kerala, India.
SASTRA Deemed University, Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, Thanjavur-613401, Tamil Nadu, India.
Phys Rev E. 2025 Apr;111(4-1):044218. doi: 10.1103/PhysRevE.111.044218.
We investigate the influence of adaptation disparity and phase lag on the heterogeneous nucleation leading to multi-step and single-step phase transitions in a finite-size adaptive network due to frequency disorders. We elucidate that the adaptation disparity predominates the effect of frequency disorder in seeding the heterogeneous nucleation. Further, a large phase lag facilitates almost a continuous spectrum of partially and fully synchronized frequency clusters, and multistability among them. We also find that the underlying mechanisms of heterogeneous nucleation due to the adaptation disparity and phase lag parameters are distinctly different from that observed only in the presence of disorders. Furthermore, we also analytically deduce the macroscopic evolution equations for the cluster dynamics using the collective coordinates framework and show that resulting reduced dynamics mimic the observed heterogeneous phase transitions of the adaptive network under adaptation disparity and phase lag. Further, we deduce the upper bound for the coupling strength for the existence of two intra-clusters explicitly in terms of the adaptation disparity and phase lag parameters for the onset of the abrupt single-step transition.
我们研究了适应差异和相位滞后对有限尺寸自适应网络中由于频率紊乱导致的多步和单步相变的异质成核的影响。我们阐明，在引发异质成核方面，适应差异主导了频率紊乱的影响。此外，大的相位滞后促进了几乎连续的部分和完全同步频率簇谱以及它们之间的多重稳定性。我们还发现，由适应差异和相位滞后参数导致的异质成核的潜在机制与仅在存在紊乱时观察到的机制明显不同。此外，我们还使用集体坐标框架解析推导了簇动力学的宏观演化方程，并表明由此产生的简化动力学模拟了自适应网络在适应差异和相位滞后下观察到的异质相变。进一步，我们根据适应差异和相位滞后参数明确推导了突然单步转变开始时两个簇内存在的耦合强度的上限。
