Extended mean-field approach for chimera states in random complex networks

Area of Science:

• Complex systems
• Nonlinear dynamics
• Network science

Background:

• Chimera states, characterized by coexisting coherent and incoherent dynamics in identical oscillators, are typically studied in Euclidean space.
• Nonlocal interactions and phase lag are known critical factors for chimera state formation in the Kuramoto model.

Purpose of the Study:

• To investigate the specific roles of nonlocal interactions and phase lag in the formation of chimera states within random network structures.
• To understand how network topology, such as degree heterogeneity and disordered connections, influences the emergence of chimera states.

Main Methods:

• Development of an extended mean-field approximation tailored for random networks.
• Numerical simulations to analyze oscillator dynamics and chimera state formation.
• Investigation across different network types, including Erdös-Rényi and regularly random networks.

Main Results:

• In Erdös-Rényi networks, chimera state emergence is primarily driven by degree heterogeneity combined with a non-zero phase lag.
• In regularly random networks, disordered connections and long-range interactions can induce chimera states even when node degrees are uniform.
• A novel dynamic state was identified where oscillator drift slows below a characteristic frequency due to connectivity disorder at large phase lags, extending beyond mean-field predictions.

Conclusions:

• Degree heterogeneity and phase lag are crucial for chimera states in random networks, particularly in Erdös-Rényi networks.
• Network connectivity disorder, not just degree distribution, plays a significant role in chimera state formation, especially with long-range interactions.
• The study reveals complex dynamics in random networks that deviate from standard mean-field approximations, highlighting the importance of topological disorder.