Explosive synchronization of multi-layer frequency-weighted coupled complex systems**Project supported by the National Natural Science Foundation of China (Grant No. 61771299), the Key Laboratory of Speciality Fiber Optics and Optical Access Networks, Shanghai University, China (Grant No. SKLSFO2012-14), Funding of the Key Laboratory of Wireless Sensor Network and Communication, Shanghai Institute of Microsystem and Information Technology, China, and Funding of the

Abstract

Synchronization is a phenomenon that is ubiquitous in engineering and natural ecosystems. The study of explosive synchronization on a single-layer network gives the critical transition coupling strength that causes explosive synchronization. However, no significant findings have been made on multi-layer complex networks. This paper proposes a frequency-weighted Kuramoto model on a two-layer network and the critical coupling strength of explosive synchronization is obtained by both theoretical analysis and numerical validation. It is found that the critical value is affected by the interaction strength between layers and the number of network oscillators. The explosive synchronization will be hindered by enhancing the interaction and promoted by increasing the number of network oscillators. Our results have importance across a range of engineering and biological research fields.