When noise decreases deterministic diffusion

Dynamical noise, acting homogeneously in each time step, can enhance the stability of an unstable fixed point. However, if dynamical noise is added locally in state space, additional clear enhancement can be achieved, if this restriction is chosen properly. A systematic analysis of the influence of local and global dynamical noise on the residence time of an unstable state is presented, and optimal parameters for the stabilizing mechanisms are discussed. As a consequence, it is demonstrated that local dynamical noise can yield increased localization in deterministic diffusion models.