Synchronization of moving oscillators in three dimensional space.

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Statistical Physics

Background:

• Investigating emergent phenomena in networks of interacting agents is crucial for understanding collective behavior.
• Random walkers with internal oscillators provide a model system for studying synchronization dynamics.

Purpose of the Study:

• To explore the macroscopic behavior and synchronization in a network of interacting random walkers with oscillators.
• To determine the conditions and stability of synchronization under varying interaction parameters.

Main Methods:

• Analytical derivation of the density-dependent threshold for synchronization using linear stability analysis.
• Numerical verification of analytical results and exploration of basin stability for robustness assessment.
• Analysis using both limit cycle and chaotic oscillators across a range of parameters (interaction strength, speed, vision range).

Main Results:

• Synchronization arises in the system depending on the nature and strength of interactions.
• A density-dependent threshold for coupling strength was analytically derived and numerically confirmed.
• Basin stability analysis revealed the robustness of the synchronous state under perturbations.

Conclusions:

• The study demonstrates that intermediate-range interactions can lead to synchronization in random walkers with oscillators.
• The findings provide insights into the critical role of interaction parameters in collective dynamics and system stability.
• The research contributes to understanding synchronization phenomena in complex dynamical networks.