Jenifer S Nirmala, Ghosh Dibakar, Muruganandam Paulsamy
Department of Physics, Bharathidasan University, Tiruchirappalli 620024, Tamil Nadu, India.
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India.
Phys Rev E. 2024 May;109(5-1):054302. doi: 10.1103/PhysRevE.109.054302.
We present a formula for determining synchronizability in large, randomized, and weighted simplicial complexes. This formula leverages eigenratios and costs to assess complete synchronizability under diverse network topologies and intensity distributions. We systematically vary coupling strengths (pairwise and three body), degree, and intensity distributions to identify the synchronizability of these simplicial complexes of the identical oscillators with natural coupling. We focus on randomized weighted connections with diffusive couplings and check synchronizability for different cases. For all these scenarios, eigenratios and costs reliably gauge synchronizability, eliminating the need for explicit connectivity matrices and eigenvalue calculations. This efficient approach offers a general formula for manipulating synchronizability in diffusively coupled identical systems with higher-order interactions simply by manipulating degrees, weights, and coupling strengths. We validate our findings with simplicial complexes of Rössler oscillators and confirm that the results are independent of the number of oscillators, connectivity components, and distributions of degrees and intensities. Finally, we validate the theory by considering a real-world connection topology using chaotic Rössler oscillators.
我们提出了一个用于确定大型、随机和加权单纯复形同步性的公式。该公式利用特征比和代价来评估在不同网络拓扑和强度分布下的完全同步性。我们系统地改变耦合强度（成对和三体）、度和强度分布，以确定这些具有自然耦合的相同振子的单纯复形的同步性。我们专注于具有扩散耦合的随机加权连接，并检查不同情况下的同步性。对于所有这些情况，特征比和代价能够可靠地衡量同步性，无需明确的连接矩阵和特征值计算。这种高效的方法提供了一个通用公式，只需通过操纵度、权重和耦合强度，就能在具有高阶相互作用的扩散耦合相同系统中操纵同步性。我们用罗斯勒振子的单纯复形验证了我们的发现，并确认结果与振子数量、连通分量以及度和强度的分布无关。最后，我们通过使用混沌罗斯勒振子考虑一个现实世界的连接拓扑来验证该理论。
