Heterogeneity induces cyclops states in Kuramoto networks with higher-mode coupling

Area of Science:

• Complex Systems
• Network Science
• Nonlinear Dynamics

Background:

• Disorder is typically viewed as detrimental to collective network dynamics.
• Recent studies indicate heterogeneity can enhance network synchronization.
• The constructive role of disorder in stabilizing cooperative patterns is under-explored.

Purpose of the Study:

• To investigate the role of frequency heterogeneity in stabilizing nontrivial cooperative patterns in oscillator networks.
• To demonstrate that heterogeneity can stabilize states that are unstable in homogeneous networks.

Main Methods:

• Analysis of Kuramoto networks with higher-mode coupling and frequency heterogeneity.
• Introduction of a mesoscopic collective coordinate approach.
• Validation in networks of Winfree and Stuart-Landau oscillators.

Main Results:

• Frequency heterogeneity induces stable cyclops and cluster states in Kuramoto networks.
• These states are typically unstable in networks with identical oscillators.
• Heterogeneity alone stabilizes these patterns across a range of detuning values.
• The stabilization mechanism is robust and observed in different oscillator models.

Conclusions:

• Frequency heterogeneity can constructively stabilize complex collective states in networks.
• This mechanism is general and applicable to various oscillator network models.
• Opens new avenues for designing multistate dynamics in heterogeneous systems.