Turing patterns on coupled phase oscillator chains with localized many-body interactions

Abstract

In this paper, coupled-phase oscillator chains with localized many-body interactions are studied. Systems have rich patterns such as chimera and twisted states. The coupled-phase oscillator chains have long-range two-body interactions and short-range three-body interactions, which respectively play the role of long-range inhibition of short-range activation, just like inhibitors and activators in traditional reaction-diffusion systems. The role of many-body interaction in the system is studied through the Turing pattern diagram and the critical point of Turing instability is obtained. After Turing instability occurs, the system will flow to twisted states and chimera states. The study indicates that long-range inhibition and short-range activation give an explanation for the formation of such coherent-incoherent modes such as chimera states, and that many-body interactions are good candidates as activators of the system.