Ring states in swarmalator systems

Abstract

Synchronization is a universal phenomenon, occurring in systems as disparate as Japanese tree frogs and Josephson junctions. Typically, the elements of synchronizing systems adjust the phases of their oscillations, but not their positions in space. The reverse scenario is found in swarming systems, such as schools of fish or flocks of birds; now the elements adjust their positions in space, but without (noticeably) changing their internal states. Systems capable of both swarming and synchronizing, dubbed swarmalators, have recently been proposed, and analyzed in the continuum limit. Here, we extend this work by studying finite populations of swarmalators, whose phase similarity affects both their spatial attraction and repulsion. We find ring states, and compute criteria for their existence and stability. Larger populations can form annular distributions, whose density we calculate explicitly. These states may be observable in groups of Japanese tree frogs, ferromagnetic colloids, and other systems with an interplay between swarming and synchronization.

A review of swarmalators and their potential in bio-inspired computing

“…Unexpectedly, the splintered phase wave was not observed. O'Keeffe, Evers, and Kolokolnikov [52] have extended (3) by allowing phase similarity to affect the spatial repulsion term, as well as the spatial attraction term (i.e. they multiply the second term in (3) by a term 1 + J 2 cos(θ j − θ i )).…”

“…Swarmalators are represented by colored dots in the (x, y) plane where the color of each dot represents its phase. The state is found by numerically integrating the governing equations in[52] with (J 1 , J 2 , K, N ) = (0, 0.8, 0, 100).…”

Sandsbots: Robots That Sync and Swarm

“…Although research on synchronization and swarming was somehow connected for some time, the mathematical model by O'Keeffe, Hong, and Strogatz [3] was presumably the first one taking into account the mutual coupling of these two phenomena. Their simulation results showed that agents using this unified model -the "swarmalators" -can form five spatio-temporal patterns, whose stability was analyzed in [26]. The model assumes continuous, delay-free coupling, which is impossible to achieve in multi-robot systems.…”

“…First we introduce how phases influence the position interactions. The demanded velocity of this phase-influenced aggregation model has the following form (similar to [26]…”

Random temporal connections promote network synchronization

“…Collective dynamics on temporal networks, in spite of their importance, were far less studied. In this regard, there was a line of work on synchronization and stability in temporal networks [10,32,[36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]. For example, moving agent networks were studied [36,37,41,45], where interactions among the agents are switched on when they are sufficiently close in the physical space.…”