Abstract
Motivated by the observation of highly unstable flowing states in suspensions of microtubules and kinesin, we analyse a model of mutually propelled filaments suspended in a solvent. The system undergoes a mean-field isotropic-nematic transition for large enough filament concentrations when the nematic order parameter is allowed to vary in space and time. We analyse the model in two contexts: a quasi-one-dimensional channel with no-slip walls and a two-dimensional box with periodic boundaries. Using stability analysis and numerical calculations we show that the interplay between non-uniform nematic order, activity, and flow results in a variety of complex scenarios that include spontaneous banded laminar flow, relaxation oscillations and chaos.