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Stability of the 1d swarmalator model in the continuum limit
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We study the 1d swarmalator model in the continuum limit. We examine the stability of its collective states which have compact support: synchrony, where the swarmalators lie in two sync dots (zero dimensional support), and the phase wave, where the swarmalators line up in a ring with uniformly spaced positions and phases (one dimensional support). The compact support imposes analytic difficulties that occur in many other swarmalator models and thus is blocking progress in the field. We show how to overcome this difficulty, deriving the two states' stability spectra exactly.
Forward citations
Cited by 2 Pith papers
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Effects of coupling range on the dynamics of swarmalators
A finite-range version of the 1D swarmalator model produces multi-dot synchronized clusters, higher-winding waves, and an active state, with many boundaries derived analytically and checked numerically.
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On forced swarmalators that move in higher-dimensional spaces
Analytic stability boundaries for pinned, split-pinned, sync-dot, and phase-locked states are derived for forced swarmalators in 2D and 3D periodic domains, extending previous 1D results.
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