Phase transitions on a multiplex of swarmalators
2023-09-08
KONGNI Steve Jauress,

LOUODOP FOTSO,

Abstract : Dynamics of bidirectionally coupled swarmalators subject to attractive and repulsive couplings is analyzed. The probability of two elements in different layers being connected strongly depends on a defined vision range π‘Ÿπ‘ which appears to lead both layers in different patterns while varying its values. Particularly, the interlayer static sync πœ‹ has been found and its stability is proven. First-order transitions are observed when the repulsive coupling strength πœŽπ‘Ÿ is very small for a fixed π‘Ÿπ‘ and, moreover, in the absence of the repulsive coupling, they also appear for sufficiently large values of π‘Ÿπ‘. For πœŽπ‘Ÿ=0 and for sufficiently small values of π‘Ÿπ‘, both layers achieve a second-order transition in a surprising two steps that are characterized by the drop of the energy of the internal phases while increasing the value of the interlayer attractive coupling πœŽπ‘Ž and later a smooth jump, up to high energy value where synchronization is achieved. During these transitions, the internal phases present rotating waves with counterclockwise and later clockwise directions until synchronization, as πœŽπ‘Ž increases. These results are supported by simulations and animations added as supplemental materials.