Convective instability in a diffusive predator–prey system

It is well known that biological pattern formation the Turing mechanism, in which a homogeneous steady state destabilized by addition of diffusion, though it stable kinetic ODEs. However, states are unstable ODEs rarely mentioned. This paper concerns reaction diffusion advection system under Neumann boundary conditions, where Our results provide stabilization strategy for same state, combination large rate and small can stabilize equilibrium. Moreover, we investigate existence stability nonconstant positive to through rigorous bifurcation analysis.