Weak-noise solution of Fokker-Planck equations with n (>2) variables: A simpler evaluation near equilibrium points

A recent approach to the quasipotential of drift-diffusion models is extended to the case of n>2 variables. The quasipotential determines the stationary probability density at weak noise, for some models even with each noise. At equilibrium points, the symmetric n-by-n matrix of its second derivatives is determined by a quadratic (Riccati) equation, and this is now replaced by a linear equation for an antisymmetric matrix of the same size. The resulting density function is unique and smooth near equilibrium points, including when the next term in the noise strength is taken into account.