Persistence of network synchronization under nonidentical coupling functions (Q2819091)

The paper investigates a diffusively coupled systems of oscillators NEWLINE\[NEWLINE \dot x_i = f(x_i) + \alpha \sum_{j=1}^n A_{ij} H_{ij} (t,x_i-x_j), \quad j=1,\dots,n, NEWLINE\]NEWLINE where \(\alpha\) is the coupling strength and \((A_{ij})\) is the adjacency matrix. In this work, the effects of the coupling functions \(H_{ij}(t,x)=H(x)+P_{ij}(t,x)\) with \(H(0)=0\) are considered.NEWLINENEWLINEThe main result of this paper provides conditions for the persistence of synchronized solutions for different coupling matrices \(A\). In particular, it is shown that Erdős-Rényi random graphs support large perturbations in the coupling function, and scale-free graphs do not allow large perturbations in the coupling function to be synchronized.