Complexity and transition to chaos in coupled Adler-type oscillators

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Statistical Physics

Background:

• Globally coupled nonlinear oscillators are widely studied, but locally coupled systems remain less explored.
• Understanding locally coupled systems is crucial for advancing complexity science.
• Previous work noted computation enhancement at the edge of chaos in similar systems.

Purpose of the Study:

• To characterize the needle region in parameter space for Adler-type oscillators with nearest-neighbor coupling.
• To investigate the diverse behaviors and dynamics within this specific parameter region.
• To analyze the nature of correlations and patterns in locally coupled oscillator systems.

Main Methods:

• Utilizing the phase approximation for weakly coupled systems.
• Detailed characterization of the needle region in the parameter space.
• Employing entropic measures and analyzing spatiotemporal diagrams.

Main Results:

• Identified distinct dynamical behaviors within the needle region.
• Observed smooth transitions in dynamics as control parameters were varied.
• Detected wave-like patterns in spatiotemporal diagrams indicating nontrivial correlations.
• Found local spatial correlation at the onset of chaos with coherent clusters and disordered boundaries.

Conclusions:

• The needle region exhibits a heterogeneous nature with complex dynamics.
• Wave-like patterns demonstrate significant spatiotemporal correlations in locally coupled oscillators.
• Coherent behavior emerges in clusters, separated by disordered interfaces, near the chaotic transition.