<p>The coexistence of clockwise and counterclockwise rotational dynamics results in chirality, which plays a critical role in shaping the behavior of coupled systems. In this study, we investigate the effects of chirality in globally coupled Stuart–Landau oscillators with competing attractive and repulsive interactions. For identical frequencies, we observe dynamical transitions from mixed synchronization to mixed oscillation death when the proportions of clockwise and counterclockwise frequencies in chiral oscillators are symmetric. Asymmetry in the proportions induces symmetry-breaking clustering, leading to a transition from cluster oscillatory states to cluster oscillation death. These transitions are confirmed through bifurcation analysis. Introducing heterogeneous frequencies reveals transitions from desynchronized states to chiral wave states and oscillation death via chimera-like dynamics. Increased heterogeneity enhances disorder, expanding regions of desynchronization and chimera-like states while reducing coherent chiral wave behaviors. Subsequently, we explore the robustness of the chimera-like state and its transitions in chiral van der Pol oscillators by incorporating heterogeneous frequencies. These findings provide insights into chirality-driven dynamics, with implications for understanding chimera phenomena, optimizing networks, and improving control strategies in complex systems.</p>

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Chirality-driven collective dynamics in oscillators with attractive and repulsive couplings

  • Sathiyadevi Kanagaraj,
  • Premraj Durairaj,
  • Zhigang Zheng

摘要

The coexistence of clockwise and counterclockwise rotational dynamics results in chirality, which plays a critical role in shaping the behavior of coupled systems. In this study, we investigate the effects of chirality in globally coupled Stuart–Landau oscillators with competing attractive and repulsive interactions. For identical frequencies, we observe dynamical transitions from mixed synchronization to mixed oscillation death when the proportions of clockwise and counterclockwise frequencies in chiral oscillators are symmetric. Asymmetry in the proportions induces symmetry-breaking clustering, leading to a transition from cluster oscillatory states to cluster oscillation death. These transitions are confirmed through bifurcation analysis. Introducing heterogeneous frequencies reveals transitions from desynchronized states to chiral wave states and oscillation death via chimera-like dynamics. Increased heterogeneity enhances disorder, expanding regions of desynchronization and chimera-like states while reducing coherent chiral wave behaviors. Subsequently, we explore the robustness of the chimera-like state and its transitions in chiral van der Pol oscillators by incorporating heterogeneous frequencies. These findings provide insights into chirality-driven dynamics, with implications for understanding chimera phenomena, optimizing networks, and improving control strategies in complex systems.