Collective synchronization of the multi-component Gross–Pitaevskii–Lohe system

Collective Dynamics of Lohe type aggregation models

“…Thus, when x0 c1 = x0 c2 = 0, the center of mass will stay steady at the origin (cf. Figure 3 (a)), which also agrees with the conclusion in Remark 4.2 of [11].…”

“…The larger κ, the smaller value 1 − R ∞ . Meanwhile, |x 1 c (t) − x 2 c (t)| also converges to zero, which could be also justified in a similar process as shown in Corollary 4.1 of [11]. take N = 6 and d = 2 in (2.2).…”

“…In fact, complete state aggregation and practical aggregation estimates do not depend on the form of the initial data and the relative L 2 -distances of the initial data play a crucial role. However, when we deal with the center-of-mass x c , we used the Gaussian initial data so that they have the symmetric form (see Remark 4.2 in [11]). For the numerical experiment, we introduce the following quantities (see [11] for details):…”

“…However, when we deal with the center-of-mass x c , we used the Gaussian initial data so that they have the symmetric form (see Remark 4.2 in [11]). For the numerical experiment, we introduce the following quantities (see [11] for details):…”

“…In [11], the authors consider nonlinearly coupled Schrödinger-Lohe type system by employing cubic nonlinearity so that the model would be reduced to the Gross-Pitaevskii equation when the coupling is turned off:…”