Collective dynamics in mobile active systems: pattern formation, synchronization, and phase transitions

Mobility is a relevant feature of many living systems in nature. Its reasons are diverse, ranging from foraging and hunting to mating, reproduction, and migration. In many such contexts, the motion of individuals gives rise to the spontaneous emergence of observable collective patterns. These patterns provide valuable information about the behavior of the system and about the mechanisms underlying their formation. Because these systems involve many interacting agents, complex networks provide a natural framework for their study. Interactions may occur between directly or indirectly connected individuals, with or without hierarchical organization or leadership. The mobility of the agents further enriches the dynamics, making these systems especially interesting from the perspective of collective behavior and emergent phenomena. Self-organization and adaptation through topological or functional changes are among the key mechanisms shaping the dynamics of these systems. In many cases, collective behavior emerges from local interactions, imitation processes, or adaptive responses to the environment. Mobility can substantially modify the effective interaction network and, consequently, alter the collective outcomes observed at the system level. Understanding these patterns is essential, as they arise in a wide variety of biological, social, and technological systems. Their study provides insight into the fundamental mechanisms driving collective phenomena, and also helps assess their predictability and controllability. This is particularly important in contexts where anticipating, enhancing, or preventing specific collective behaviors may be desirable. More recently, ”swarmalators” have attracted significant attention as a particularly rich class of mobile interacting units. These systems combine spatial dynamics with phase dynamics and display characteristic features such as decentralized control, selforganization, indirect communication, and emergent behavior. They are also often highly sensitive to parameters and initial conditions. Synchronization has long been one of the central concepts in the study of dynamical systems for the last 50 years, especially since Kuramoto introduced an order parameter to characterize collective coherence as synchronization. Mobile interacting systems have naturally extended this line of research and revealed a remarkably rich variety of spontaneous collective behaviors arising without external control. The interplay between motion, interaction, adaptation, and synchronization gives rise to a wide spectrum of dynamical regimes and phase transitions that are still far from fully understood. Identifying the mechanisms that drive these transitions, and clarifying their nature, remains one of the key challenges in the field. Topics of interest for this article collection include, but are not limited to:• Collective motion and swarm intelligence • Mobile and adaptive systems • Self-organization and pattern formation • Agent-based and multi-scale modeling • Learning and adaptation in collective systems • Social, biological, and technological networks • Applications to robotics, transportation, and social systems Topic editors: Patrick Herve Louodop Fotso, Albert Diaz-Guilera, Hilda Cerdeira Source: https://www.frontiersin.org/research-topics/80315/collective-dynamics-in-mobile-active-systems-pattern-formation-synchronization-and-phase-transitions