Synchronization and spatial patterns in forced swarmalators.

Area of Science:

• Physics
• Complex Systems
• Statistical Mechanics

Background:

• Swarmalators combine coordinated spatial movement with internal phase synchronization, analogous to Kuramoto oscillators.
• External periodic stimuli can influence the synchronization dynamics of such systems.
• Understanding swarmalator behavior under external forces is crucial for modeling collective phenomena.

Purpose of the Study:

• To investigate the impact of a two-dimensional external periodic stimulus on swarmalator systems.
• To analyze how stimulus intensity affects phase synchronization and spatial-behavior correlation.
• To identify emergent patterns and dynamics in response to varying external forces.

Main Methods:

• Simulating a system of two-dimensional swarmalators subjected to an external periodic force.
• Analyzing phase synchronization and the correlation between particle phases and spatial locations.
• Characterizing emergent spatial patterns, including aggregation, spiraling, and cluster formation.

Main Results:

• External forces synchronize swarmalator phases and angular velocities with the stimulus frequency.
• Increasing force intensity reduces phase-spatial correlation, leading to a loss of coordinated movement at critical values.
• Emergent patterns include static circular distributions, stable spirals, and dynamic two-cluster formations with particle exchange or collisions.

Conclusions:

• External periodic stimuli can effectively synchronize swarmalator internal dynamics.
• The interplay between stimulus intensity and swarmalator parameters dictates the emergence of complex spatial patterns.
• Swarmalator systems exhibit rich collective behaviors, transitioning from synchronized motion to diverse aggregative and dynamic patterns under external influence.