Chaos-generating periodic orbits of topological defects in confined active nematics

Active nematics in two dimensions stir themselves efficiently through internally generated chaotic flows, largely driven by motile [Formula: see text] disclinations.We investigate how this tendency toward chaotic fluid stirring can, counterintuitively, produce certain ordered, periodic flows in confinement, characterized by stable periodic orbits of [Formula: see text] disclinations. We computationally study two-dimensional active nematics in systems with boundary conditions requiring a prescribed number n of excess [Formula: see text] disclinations, using Beris-Edwards nematohydrodynamics simulations alongside an agent-based simulation approach. We find that when confinement is sufficiently strong to prevent defect pair-nucleation, but not strong enough to arrest all flow, then [Formula: see text] defects generically follow a "golden braid" orbit as observed recently in experiments, and we predict a "silver braid" orbit of [Formula: see text] defects. For these results and for greater numbers of defects, we show that the periodic or chaotic nature of the dynamics is determined by a balance between the number of defects and the number of vortices in the flow field, suggesting a design criterion for ordered flows in active nematics.