Effects of Noise on Nonlinear Dynamics

Abstract

The influence of noise on nonlinear dynamical systems is a very important area of research, since all systems, physiological and other, evolve in the presence of noisy driving forces. It is often thought that noise has only a blurring effect on the evolution of dynamical systems. It is true that that can be the case, especially for so-called “observational” or “measurement” noise, as well as for linear systems. However, in nonlinear systems with dynamical noise, i.e., with noise that acts as a driving term in the equations of motion, noise can drastically modify the deterministic dynamics. For example, the hallmark of nonlinear behavior is the bifurcation, which is a qualitative change in the phase space motion when the value of one or more parameter changes.