Collective behavior of non-reciprocal swarmalators

Non-reciprocal interactions play a crucial role in complex systems, but their effects on agent systems with phase coupling are not yet fully understood. This paper explores the impact of non-reciprocality on collective behavior in the swarmalator model, focusing on two types of non-reciprocal coupling mechanisms: leadership and autonomous. Leadership coupling involves a few “leaders” exerting one-way interventions on the group, significantly altering the patterns of collective movement. Autonomous coupling emphasizes individuals actively adjusting their interaction intensity with others based on their own states, enhancing the system’s flexibility and adaptability. These mechanisms lead to diverse dynamic states such as translational synchrony, oscillatory asynchrony, and chimera state. Through numerical simulations and statistical analysis, the study reveals how non-reciprocal interactions drive complex collective behaviors and demonstrates the dynamic evolution in different parameter spaces.