Transient behaviour of heterogeneous diffusion processes in the cubic potential

The noise to signal transition is a very significant process in physics and plays an important role in the study of unstable cubic potentials. We extend the unstable external force field to a heterogeneous environment and theoretically analyze stochastic noise-to-signal transition of overdamped Brownian motion of a particle in it. We obtained a proportional relationship between SNR and heterogeneity in the view of standard statistical method. However, When the new local statistical methods are introduced, the relationship between SNR and heterogeneity is diametrically opposed to the previous. For this reason we have given a certain physical explanation.