Chimera States in Wheel Networks

TL;DR

This paper investigates how higher-order interactions affect the emergence and stability of chimera states in networks of coupled chaotic oscillators, revealing their significant influence across different coupling schemes and oscillator types.

Contribution

It introduces a systematic classification method for dynamical behaviors in wheel networks with higher-order interactions and demonstrates their impact on chimera states across multiple models.

Findings

Higher-order interactions can enhance or suppress chimera states.

The influence of higher-order interactions depends on the coupling scheme and oscillator dynamics.

Chimera states are more prevalent and robust under certain higher-order interaction conditions.

Abstract

How higher-order interactions influence dynamical behavior in networks of coupled chaotic oscillators remains an open question. To address this, we investigate emergent dynamical behaviors in a wheel network of R\"ossler and Lorenz oscillators that incorporates both pairwise (1-simplex) and higher-order (2-simplex) interactions under three coupling schemes, namely, diffusive, conjugate, and mean-field diffusive coupling. Our numerical analysis reveals four distinct collective behaviors: synchronization, desynchronization, chimera states, and synchronized clusters. To systematically classify these dynamical behaviors, we introduce two statistical measures that effectively capture synchronization patterns among arbitrarily positioned nodes. Applying these measures across all dynamical models and coupling schemes (six different models in total), we show that both pairwise and higher-order interactions crucially influence the emergence and robustness of chimera states. We observe that under pairwise interaction alone, chimera states appear with high prevalence in specific coupling ranges, though the robustness depends on both the coupling scheme and the underlying dynamical system. Incorporation of higher-order interactions reveals that the higher-order interaction underlying diffusive coupling enhances chimera states in both R\"ossler and Lorenz networks; under conjugate coupling, it strengthens chimera states in Lorenz but instead promotes full synchronization in R\"ossler; and under mean-field diffusive coupling, higher-order interactions generally favor synchronization, particularly for R\"ossler oscillators, but promote chimera in the Lorenz system for the intermediate range of its strengths. Overall, our results demonstrate that higher-order interactions can significantly modulate, promote, or suppress chimera states depending on the coupling mechanism and oscillator dynamics.