Bifurcation solutions in the diffusive minimal sediment

Abstract This paper is concerned with the diffusive minimal sediment model with no-flux boundary conditions. The steady-state bifurcation with two-dimensional kernel is firstly obtained with respect to this model by the space decomposition and the implicit function theorem. The existence of the Hopf bifurcation is next attained, and the direction and the stability of the Hopf bifurcation are analyzed in detail. Numerical simulations are done to support and complement the theoretical results.