Before revision:  These dynamical systems closely resemble a Hamiltonian system in \Bbb R^{2n}, but with the canonical equation for one of the variables in each conjugate pair rescaled by a ratio of the diffusion coefficients. The ratio therefore measures the obstruction preventing a two-component feedback loop from being Hamiltonian (where the ratio equals one) .
After revision:  These dynamical systems closely resemble a Hamiltonian system in \Bbb R^{2n}, but with the canonical equation for one of the variables in each conjugate pair rescaled by a number called the Turing instability parameter. The Turing instability parameter therefore measures the obstruction preventing a two-component feedback loop from being Hamiltonian (where the ratio equals one) .