Spatially homogeneous equilibrium
= Spatially homogeneous equilibrium
A spatially homogeneous equilibrium of a <reaction–diffusion system> is a constant state $u_*$ satisfying $f(u_*)=0$. Since its spatial derivatives vanish, its stability to homogeneous perturbations is determined by the <Jacobian matrix> $Df(u_*)$; diffusion can additionally destabilize nonconstant modes.