Complete Synchronization of Coupled Oscillators Based on the Contraction Theory
Abstract
This paper studies contraction theory with the aim of exploring complete synchronization phenomenon in complex networks of coupled oscillators. We examine the conditions for complete synchronization in three network topologies: all-to-all, star, and ring. Specifically, we derive the conditions under which networks of linearly coupled (Duffing) van der Pol oscillators achieve complete synchronization. Additionally, by combining contraction theory with the trapping region method, we identify the conditions for complete synchronization of networks of linearly coupled Rayleigh van der Pol oscillators under specific initial conditions.
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