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We use linear stability analysis and hybrid lattice Boltzmann simulations tostudy the dynamical behaviour of an active nematic confined in a channel madeof viscoelastic material. We find that the quiescent, ordered active nematic isunstable above a critical activity. The transition is to a steady flow statefor high elasticity of the channel surroundings. However, below a thresholdelastic modulus, the system produces spontaneous oscillations with periodicflow reversals. We provide a phase diagram that highlights the region wheretime-periodic oscillations are observed and explain how they are produced bythe interplay of activity and viscoelasticity. Our results suggest newexperiments to study the role of viscoelastic confinement in thespatio-temporal organization and control of active matter.

Viscoelastic confinement induces periodic flow reversals in active nematics