Delay induced double explosive transition in a swarmalator system.

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Mathematical Biology

Background:

• Synchronization and aggregation are ubiquitous phenomena observed in various natural and artificial systems.
• Swarmalator systems, which model interacting agents, have garnered recent scientific attention.
• The impact of time delays on swarmalator dynamics remains underexplored, despite their potential to introduce complex behaviors.

Purpose of the Study:

• To investigate the effects of incorporating a phase delay into the internal dynamics of swarmalator systems.
• To explore the novel synchronization patterns and transitions that emerge in delayed swarmalator models.
• To establish a foundation for understanding how environmental factors influencing delay impact mathematical models.

Main Methods:

• Development of a delayed swarmalator model with a focus on internal phase dynamics.
• Analysis of system behavior across various parameter spaces and domains.
• Utilizing the local and complex order parameter to characterize emergent dynamics.

Main Results:

• Discovery of unique phenomena such as the 'boiling chimera' state and 'ring static synchronization'.
• Identification of a double explosive transition: synchronous to asynchronous, then asynchronous to synchronous states.
• Demonstration that phase delay significantly enriches the dynamic repertoire of swarmalator systems.

Conclusions:

• The inclusion of phase delay in swarmalator models leads to fundamentally new collective behaviors and transitions.
• These findings provide insights into phenomena relevant to understanding brain diseases characterized by altered synchronization.
• This work underscores the importance of considering environmental delays in mathematical modeling for increased realism.