Theorem: Cayley-Hamilton of Turing J gives zero matrix; det(M(43/20)) = -1809/40 < 0 (Turing instability)

Theorem (Cayley-Hamilton Turing-dispersion canonical): for Jacobian J = [[5, -6], [6, -7]] with tr(J) = -2, det(J) = 1, and diffusion D = diag(1, 10), the Cayley-Hamilton identity J^2 - tr(J) J + det(J) I = zero-matrix holds exactly, and…