Bubbling in Oscillator Networks

Abstract

A network of coupled time-varying systems, where individual nodes are interconnected through links, is a modeling framework widely used by many disciplines. For identical nodes displaying a complex behavior known as chaos, clusters of nodes or the entire network can synchronize for a range of coupling strengths. Here, we demonstrate that small differences in the nodes give rise to desynchronization events, known as bubbling, in regimes where synchronization is expected. Thus, small unit heterogeneity in all real systems has an unexpected and outsized effect on the network dynamics. We present a theoretical analysis of bubbling in chaotic oscillator networks and predict when bubble-free behavior is expected. Our work demonstrates that the domain of network synchronization is much smaller than expected and is replaced by epochs of synchronization interspersed with extreme events. Our findings have important implications for real-world systems where synchronized behavior is crucial for system functionality.