Multibranch entrainment and slow evolution among branches in coupled oscillators.

Area of Science:

• Complex systems
• Nonlinear dynamics
• Statistical physics

Background:

• Globally coupled oscillators often exhibit multibranch entrainment (MBE), characterized by numerous stable states.
• MBE's existence has been linked to strong higher harmonics in coupling functions, suggesting system nonergodicity.
• This apparent nonergodicity seems to contradict fundamental principles of statistical physics due to microscopic energy barriers.

Purpose of the Study:

• To investigate the ergodicity of globally coupled oscillators exhibiting multibranch entrainment.
• To reconcile the phenomenon of MBE with principles of statistical physics.
• To elucidate the dynamics of systems with a large number of stable states.

Main Methods:

• Application of macroscopic dynamical theories.
• Analysis of system evolution under the influence of thermal noise.
• Investigation of energy barriers and state transitions.

Main Results:

• Demonstration that globally coupled oscillators do not exhibit true ergodicity breaking.
• Observation of slow system evolution among branch states.
• Identification of thermal noise as a driver for jumping over microscopic energy barriers.

Conclusions:

• The apparent nonergodicity in MBE systems is explained by slow dynamics along a neutrally stable manifold.
• Thermal noise plays a crucial role in system evolution, allowing transitions between numerous stable states.
• The study provides a framework for understanding complex dynamics in systems with many coexisting states.