Dynamic patterns and phase transitions in confined active particle systems

The persistent assembly and clustering in active systems, ranging from biological aggregates to synthetic active matter, is governed by the interplay of self-propulsion, environmental stimulus, and interparticle interactions. This study investigates how self-propelled particles (SPPs) dynamically organize around spatially distributed attractive points, which act as targets for directed motion. The systematic variation of alignment sensitivity, particle number, and noise reveal distinct regimes of cluster formation and stability. At low noise levels, particles exhibit coherent alignment toward attractors, forming dynamic rotating clusters whose behavior is highly sensitive to alignment rate. Increasing alignment strength along with the number of SPPs breaks rotational symmetry leading to ordered phases, while noise introduces disordered or transient phases. Single-particle motion in the presence of convex quadrilateral arrangement of attractive points reveals patterns reminiscent of deterministic limit cycles, with alignment strength acting as a tuning parameter for spatial oscillations. In the case of multiple SPPs we identify three regions depending on the strength of the aligning angular momentum and number of SPPs as disordered, ordered rotating cluster, and ordered static clusters. We observe a weakly second-order phase transition from a disordered phase to an ordered phase. The study reveals how active particles exhibit some order around competing environmental cues such as food sources.