Remarks on the Schrodinger-Lohe model

Abstract

In this thesis, we study the asymptotic behavior of the coupled Schrodinger-Lohe system under the same one-body potential with a special communication network between particles. First, we review the previous results on the classical all-to-all Schrodinger-Lohe system and the relation between the Schrodinger-Lohe system and Lotka-Volterra system. Then, we present a large-time behavior of the system by introducing the pairwise correlation function. Furthermore, we provide the existence of equilibria for the finite-dimensional system under the general network framework. Finally, we provide several numerical simulation results supporting our analytical result.