Confined active nematics exhibit rich dynamical behavior, including spontaneous flows, periodic defect dynamics, and chaotic `active turbulence. Here, we study these phenomena using the framework of Exact Coherent Structures, which has been successful in characterizing the routes to high Reynolds number turbulence of passive fluids. Exact Coherent Structures are stationary, periodic, quasiperiodic, or traveling wave solutions of the hydrodynamic equations that, together with their invariant manifolds, serve as an organizing template of the dynamics. We compute the dominant Exact Coherent Structures and connecting orbits in a pre-turbulent active nematic channel flow, which enables a fully nonlinear but highly reduced order description in terms of a directed graph. Using this reduced representation, we compute instantaneous perturbations that switch the system between disparate spatiotemporal states occupying distant regions of the infinite dimensional phase space. Our results lay the groundwork for a systematic means of understanding and controlling active nematic flows in the moderate to high activity regime.
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