Exploring synchronizability of complex dynamical networks from edges perspective

With the rapid development of network information technology, synchronization problem of complex dynamical networks has garnered extensive attention. Current research predominantly concentrates on analyzing synchronizability and synchronization control in the complex dynamical networks with static edge weights or single weight attribute connections. However, there is limited research on networks characterized by variable weights and multiple weighted connections. This study addresses this gap by analyzing the synchronizability of such complex networks. In this paper, we investigate the synchronizability of two types of networks: weight-variable complex dynamical networks and multi-weighted complex dynamical networks. Considering the evolution of network weights, the synchronizability of complex dynamical network with weight-variable is investigated, the master stability equation, synchronizability criteria of the network are derived, and experiments are used to substantiate the validity of our findings. Our study then shifts to multi-weighted complex networks. Take the Rössler oscillators as node dynamics, we explore the impact of different inner coupling matrices on synchronization types under both unknown and known topologies. Moreover, we extend our study to scenarios with different coupling strengths. The analysis reveals that the inner coupling matrix influences the network’s synchronization region type. Interestingly, the clarity or ambiguity of network topologies does not markedly affect the synchronization region type. Furthermore, our analysis indicates a correlation between the synchronization region boundaries of multi-weighted complex networks and those of their single-weighted counterparts capable of synchronization.