Extensive multistability and scalings in coupled phase oscillators with pairwise or non-pairwise interactions.

Area of Science:

• Complex systems
• Nonlinear dynamics
• Network science

Background:

• Coupled oscillator systems commonly exhibit multistability and abrupt desynchronization.
• These phenomena are often attributed to non-pairwise interactions.
• Understanding the role of different coupling strategies is crucial.

Purpose of the Study:

• To systematically compare three distinct coupling strategies in phase oscillator systems.
• To investigate how higher-order coupling modes and adaptive coupling influence macroscopic behaviors.
• To develop a theoretical framework explaining the dynamic origins of multistability and desynchronization.

Main Methods:

• Systematic comparison of three coupling strategies.
• Development of a theoretical framework.
• Analysis of dynamic origins, mechanisms, and critical scaling relationships.

Main Results:

• Adaptive and second-order coupling enable multistability and abrupt desynchronization in pairwise coupled systems.
• Mechanisms underlying multistability and irreversible desynchronization transitions were clarified.
• Critical scaling relationships between order parameters and coupling strength were explored.

Conclusions:

• Higher-order interactions are not strictly necessary for complex behaviors in coupled oscillators.
• Adaptive and second-order coupling provide alternative pathways to multistability and abrupt desynchronization.
• The theoretical framework offers insights into the dynamics of complex oscillator networks.