  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.
