Topologically-induced suppression of explosive synchronization

Abstract: Nowadays, explosive synchronization is a well documented phenomenon occurring in networks when the node frequency and its degree are correlated. This first-order transition, which may coexists with classical synchronization, has been recently causally linked to some pathological brain states like epilepsy and fibromyalgia. It is then intriguing how most of neuronal systems can operate in normal conditions avoiding explosive synchronization. Here, we have discovered that synchronization in networks where the oscillators are coupled via degree-biased Laplacian operators, naturally controls the transition from explosive to standard synchronization in neuronal-like systems. We prove analytically that explosive synchronization emerges when using this theoretical setting in star-like (neuronal) networks. As soon as this star-like network is topologically converted to a network containing cycles, e.g., via synaptic connections to other neurons, the explosive synchronization gives rise to classical synchronization. This allows us to hypothesize that such topological control of explosive synchronization could be a mechanism for the brain to naturally work in normal, non-pathological, conditions.