Chaos in generically coupled phase oscillator networks with nonpairwise interactions

Area of Science:

• Complex systems
• Nonlinear dynamics
• Network science

Background:

• The Kuramoto-Sakaguchi model describes coupled phase oscillators with pairwise interactions.
• Identical, globally coupled oscillators exhibit simple dynamics: full synchrony or splay phase.
• Bifurcations between these states are highly degenerate in the standard model.

Purpose of the Study:

• To investigate emergent dynamics in phase oscillator networks with non-pairwise coupling.
• To explore the impact of higher-order interactions (three- and four-way) on network behavior.
• To demonstrate the emergence of complex dynamics, including chaos, in minimal systems.

Main Methods:

• Normal-form based calculations to derive higher-order coupling terms.
• Analysis of symmetric phase oscillator networks with non-pairwise interactions.
• Investigation of the smallest possible network dimension (four coupled oscillators).

Main Results:

• Non-pairwise coupling, including three- and four-way interactions, introduces complex emergent dynamics.
• Chaos is shown to appear in a four-oscillator network for specific parameter ranges.
• Symmetric phase oscillator networks exhibit richer behaviors beyond simple synchrony or asynchrony.

Conclusions:

• Higher-order, non-pairwise interactions are crucial for complex dynamics in oscillator networks.
• The standard Kuramoto-Sakaguchi model's simplicity is overcome by including these higher-order terms.
• Chaos can emerge in minimal coupled oscillator systems when non-pairwise coupling is considered.