Chimera States in Three Populations of Pendulum-Like Elements with Inertia

Hao Yin

doi:10.11648/j.ajpa.20190701.15

Abstract

The aim of this study is to investigate the chimera states in three populations of pendulum-like elements with inertia in varying network topology. Considering the coupling strength between oscillators within each population is stronger than the inter-population coupling, we search for the chimera states in three populations of pendulum-like elements under the ring and the chain structures by adjusting the inertia and the damping parameter. The numerical evidence is presented showing that chimera states exist in a narrow interval of inertia in ring and chain structures. It is found that chimera states cease to exist with the decreasing of damping parameter. Furthermore, it is revealed that there is a linear relationship between the inertia (m) and damping parameter threshold (eth) in the two network structures.

Highlights

The phenomenon of chimera states in the network of coupled, identical oscillators has attracted a great deal of theoretical and experimental interest
We have discovered that chimera states exist in both ring and chain structures, and it will disappear with increasing inertia m
The appearance of chimera states in three populations in the ring and the chain network structures composed of three populations by adjustment of inertia m and damping parameter ε is investigated

Summary

Introduction

The phenomenon of chimera states in the network of coupled, identical oscillators has attracted a great deal of theoretical and experimental interest It corresponds to the spatiotemporal patterns, in which some oscillators exhibit coherent dynamics while the others are incoherent in the system. Considering the oscillators within each population are coupled stronger than the neighboring populations and the oscillators oscillate at the same natural frequency and fixed phase lag, we discuss the variations of chimera states by adjusting the inertia and the damping parameter. We follow previous studies on chimera states [18] and set the coupling strength between the oscillators within each population Kσσ ' = 0.6 , while neighboring populations couple with weaker strength Kσσ ' = 0.4 , such that the inter-population coupling is weaker than the coupling within each subpopulation In this system, we keep N = 64 , d1 = d2 = d3 = 0 , and α = π 2 − 0.05 constant and adjust ε between 0 and 1. In following simulations we use random initial conditions for oscillators in each population within (0, 2π )

Numerical Simulations and Discussions

Conclusions