TY - JOUR

T1 - Chimera dynamics of generalized Kuramoto-Sakaguchi oscillators in two-population networks

AU - Lee, Seungjae

AU - Krischer, Katharina

N1 - Publisher Copyright:
© 2023 The Author(s). Published by IOP Publishing Ltd.

PY - 2023/10/6

Y1 - 2023/10/6

N2 - Chimera dynamics, an intriguing phenomenon of coupled oscillators, is characterized by the coexistence of coherence and incoherence, arising from a symmetry-breaking mechanism. Extensive research has been performed in various systems, focusing on a system of Kuramoto-Sakaguchi (KS) phase oscillators. In recent developments, the system has been extended to the so-called generalized Kuramoto model, wherein an oscillator is situated on the surface of an M-dimensional unit sphere, rather than being confined to a unit circle. In this paper, we exploit the model introduced in Tanaka (2014 New. J. Phys. 16 023016) where the macroscopic dynamics of the system was studied using the extended Watanabe-Strogatz transformation both for real and complex spaces. Considering two-population networks of the generalized KS oscillators in 2D complex spaces, we demonstrate the existence of chimera states and elucidate different motions of the order parameter vectors depending on the strength of intra-population coupling. Similar to the KS model on the unit circle, stationary and breathing chimeras are observed for comparatively strong intra-population coupling. Here, the breathing chimera changes their motion upon decreasing intra-population coupling strength via a global bifurcation involving the completely incoherent state. Beyond that, the system exhibits periodic alternation of the two order parameters with weaker coupling strength. Moreover, we observe that the chimera state transitions into a componentwise aperiodic dynamics when the coupling strength weakens even further. The aperiodic chimera dynamics emerges due to the breaking of conserved quantities that are preserved in the stationary, breathing and alternating chimera states. We provide a detailed explanation of this scenario in both the thermodynamic limit and for finite-sized ensembles. Furthermore, we note that an ensemble in 4D real spaces demonstrates similar behavior.

AB - Chimera dynamics, an intriguing phenomenon of coupled oscillators, is characterized by the coexistence of coherence and incoherence, arising from a symmetry-breaking mechanism. Extensive research has been performed in various systems, focusing on a system of Kuramoto-Sakaguchi (KS) phase oscillators. In recent developments, the system has been extended to the so-called generalized Kuramoto model, wherein an oscillator is situated on the surface of an M-dimensional unit sphere, rather than being confined to a unit circle. In this paper, we exploit the model introduced in Tanaka (2014 New. J. Phys. 16 023016) where the macroscopic dynamics of the system was studied using the extended Watanabe-Strogatz transformation both for real and complex spaces. Considering two-population networks of the generalized KS oscillators in 2D complex spaces, we demonstrate the existence of chimera states and elucidate different motions of the order parameter vectors depending on the strength of intra-population coupling. Similar to the KS model on the unit circle, stationary and breathing chimeras are observed for comparatively strong intra-population coupling. Here, the breathing chimera changes their motion upon decreasing intra-population coupling strength via a global bifurcation involving the completely incoherent state. Beyond that, the system exhibits periodic alternation of the two order parameters with weaker coupling strength. Moreover, we observe that the chimera state transitions into a componentwise aperiodic dynamics when the coupling strength weakens even further. The aperiodic chimera dynamics emerges due to the breaking of conserved quantities that are preserved in the stationary, breathing and alternating chimera states. We provide a detailed explanation of this scenario in both the thermodynamic limit and for finite-sized ensembles. Furthermore, we note that an ensemble in 4D real spaces demonstrates similar behavior.

KW - collective dynamics

KW - coupled oscillators

KW - synchronization

UR - http://www.scopus.com/inward/record.url?scp=85173229554&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/acf4d6

DO - 10.1088/1751-8121/acf4d6

M3 - Article

AN - SCOPUS:85173229554

SN - 1751-8113

VL - 56

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 40

M1 - 405001

ER -