Turing instability: oscillating chemical waves from two reacting species.
Brusselator: du/dt = Du∇²u + a − (b+1)u + u²v, dv/dt = Dv∇²v + bu − u²v. The homogeneous steady state u*=a, v*=b/a is unstable when b > 1+a². Turing instability (Du≪Dv) creates stationary spatial patterns; limit cycles create traveling waves.