Explosive synchronization in weighted complex networks

Abstract

The emergence of dynamical abrupt transitions in the macroscopic state of a system is currently a subject of the utmost interest. Given a set of phase oscillators networking with a generic wiring of connections and displaying a generic frequency distribution, we show how combining dynamical local information on frequency mismatches and global information on the graph topology suggests a judicious and yet practical weighting procedure which is able to induce and enhance explosive, irreversible, transitions to synchronization. We report extensive numerical and analytical evidence of the validity and scalability of such a procedure for different initial frequency distributions, for both homogeneous and heterogeneous networks, as well as for both linear and nonlinear weighting functions. We furthermore report on the possibility of parametrically controlling the width and extent of the hysteretic region of coexistence of the unsynchronized and synchronized states.

The Kuramoto model in complex networks

“…218 imposed in [268] is exactly the same condition |ω i − ω j | > ω c analytically found to obtain first-order transitions in star-graphs [249]. Motivated by these findings that explosive synchronization is achievable for any frequency distributions, Leyva et al [251] further analysed the following modelθ…”

“…29(b). The correlation s i ∼ ω i spontaneously emerges as a consequence of the weighting procedure [251], in contrast with the correlation between frequencies and degrees considered in [30], where such constraint is imposed in order to yield discontinuous transitions. In fact, the dependence of s on ω can be explicitly obtained for a fully connected graph.…”

Disorder induces explosive synchronization

“…[16]. Subsequently, significant attention has been paid to the further exploration of degree-frequency correlations [17][18][19][20] and in particular explosive synchronization [21][22][23][24][25][26][27][28][29][30][31][32]. While this research has augmented our understanding of explosive synchronization and its relationship with dynamical and structural correlations, in each case strong conditions are necessarily imposed on either the heterogeneity of the network, its link weights, or its initial construction to engineer first-order phase transitions.…”

Effects of frustration on explosive synchronization

“…In Figs. 6(a) and 6(f), the empty line represents hysteresis, which is a remarkable characteristic of the first-order phase transition proposed in previous studies [12][13][14][15][16][17][18][19][20]. As shown in Fig.…”

“…Zhu et al [16] showed that explosive synchronization can only occur when both the degrees and frequencies of the network's nodes are disassortative. Furthermore, the frequency-weighted phase oscillator model can also lead to explosive synchronization [17][18][19][20].…”