Self-organized bistability on globally coupled higher-order networks.

Area of Science:

• Complex systems
• Network science
• Theoretical physics

Background:

• Self-organized bistability (SOB) describes systems near a critical first-order transition, capable of shifting between states via parameter self-regulation.
• SOB has been observed in scale-free networks as recurrent transitions to transient global synchronization.

Purpose of the Study:

• To theoretically extend the concept of SOB to higher-order networks (simplicial complexes).
• To investigate the influence of coupling constraints on SOB dynamics within these complex structures.

Main Methods:

• Application of Ott-Antonsen dimensionality reduction in the thermodynamic limit for higher-order networks.
• Derivation of SOB conditions under coupling limitations.
• Numerical simulations on finite-size systems for validation.
• Analysis of continuous synchronization diagrams and spontaneous synchronized events.

Main Results:

• Derived theoretical requirements for SOB in higher-order networks under coupling constraints, showing good agreement with simulations.
• Demonstrated the critical role of SOB in initiating and terminating temporary synchronized events.
• Observed that under weak-coupling conditions, these spontaneous events exhibit statistical similarities to epileptic brain activity.

Conclusions:

• SOB is a fundamental mechanism for transient synchronization in higher-order networks, even under coupling constraints.
• The theoretical framework accurately predicts SOB behavior and its role in emergent dynamics.
• The findings offer insights into complex system dynamics, with potential parallels to biological systems like the epileptic brain.