Phase lagged coupled Kuramoto oscillators on simplicial complexes

Abstract

The study of explosive synchronization in higher-order interactions has been of keen interest among many researchers. There have been several models for higher-order interactions, here we consider the 2-simplex 2θi model with the phase lag parameter introduced to see how it affects the dynamics and thereby the critical coupling of the system. The present work is a generalization of the previous one where the study was limited to the case of vanishing α and symmetric distribution of ωi. As in the previous case(Work which has already been done by Per Sebastion Skardal and Alex Arenas), a particular macroscopic solution of steady rotation is found, which branches off the trivial solution at some positive K. For pairwise Globally coupled networks with phase frustration work has been done by Sakaguchi and Kuramoto in 1986. Here we present an analysis of the collective dynamics of a 2-simplicial system with non-zero phase lag. In the later chapters, we also present the analytics of the 2θj model in the presence of pair-wise interactions among the oscillators in which we see that along with the transition point nature of transition also changes on varying ϕ.