Rojni oscilatorji: povezava med sinhronizacijo in kolektivnim gibanjem

slovenian

2026

volume 73, issue 1

collective motion   nonlinear dynamics   self-organization   synchronization

Društvo matematikov, fizikov in astronomov

Synchronization and collective motion are among the most recognizable forms of selforganization in nature. From cardiac cells and neural rhythms to swarms of insects and flocks of fish or birds, global, ordered patterns emerge spontaneously from simple local interactions. Although synchronization and collective motion were long studied as separate phenomena, a new class of models, known as swarmalators, unifies them within a single dynamical framework. Swarmalators are agents with internal phase dynamics in which synchronization and collective motion are bidirectionally coupled. Consequently, phase differences influence spatial interactions, while spatial proximity affects the strength of phase synchronization. The purpose of this article is to provide a systematic presentation of the basic mathematical model of swarmalators, their dynamical behavior, and the characteristic collective regimes it exhibits. We explain the role of key terms and parameters of the model and illustrate the diversity of emergent dynamical patterns. In addition to qualitative descriptions, we introduce quantitative order parameters that enable a clear distinction between different dynamical states. The article is intended as a professional overview of an established model that offers valuable insight into self-organized phenomena and serves as a useful starting point for the study of complex and dynamical systems, including in a didactic context.

06.10.2026