Bifurcation analysis of spontaneous flows in active nematic fluids

Continuum models of active nematic gels have proved successful to describe a number of biological systems consisting of a population of rodlike motile subunits in a fluid environment. One of the prominent features of active systems is their ability to sustain, above a critical threshold of the active parameter, an autonomous collective motion that results in a spontaneous flow of particles. In this paper we show that in a simple channel geometry, the characteristics of this spontaneous motion are largely independent of the model that is used to describe the dynamics of the active system, but are dictated by material symmetry. The natural symmetry for active nematics in a channel is found to be described by the Klein four-group K-4 similar or equal to Z(2)XZ(2) . We perform a Lyapunov-Schmidt reduction and an equivariant bifurcation analysis to show that the K-4-equivariance of the problem generically results in two pitchfork bifurcations with four solution branches.