Synchronization stability in simplicial complexes of near-identical systems
Fatemeh Parastesh, Mahtab Mehrabbeik, Karthikeyan Rajagopal, Sajad Jafari, Matjaž Perc, Charo I. del Genio, Stefano Boccaletti
Abstract
Assessing the stability of synchronization is a fundamental task when studying networks of dynamical systems. However, this becomes challenging when the coupled systems are not exactly identical, as is always the case in practical settings. Here we introduce an extension of the Master Stability Function to determine near-synchronization stability within simplicial complexes of nearly identical systems coupled by synchronization-noninvasive functions. We validate our method on a simplicial complex of Lorenz oscillators, finding a good correspondence between the predicted regions of stability and those observed via direct simulation. This confirms the correctness of our approach, making it a valuable tool for the evaluation of real-world systems, in which differences between the constitutive elements are unavoidable.