The video shows the evolution of a solution (u,v) to a reaction-diffusion system
u_t = gamma*f(u,v) + u_xx, t &gt 0, 0 &lt x &lt pi,
v_t = gamma*g(u,v) + d*v_xx, t &gt 0, 0 &lt x &lt pi,
where pi=3.1415..., which is subject to Neumann boundary conditions
u_x = v_x = 0 at x=0 or x=pi,
and initial conditions
u(x,t=0) = u_0(x), v(x,t=0) = v_0(x), 0 &lt x &lt pi.
The reaction terms are given by the Schnakenberg reaction kinetics [1]:
f(u,v) = a - u + u^2 v
g(u,v) = b - u^2 v
All parameters (a,b,gamma,d) are provided inset.
The reaction-diffusion system has a unique spatially homogeneous steady state, which is stable with respect to spatially homogeneous perturbations.
However, Turing's instability occur...