EFFECTS OF NOISE ON THE PHASE DYNAMICS OF NONLINEAR OSCILLATORS

Various properties of human rhythmic movements have been successfully modeled using nonlinear oscillators. However, despite some extensions towards stochastical differential equations, these models do not compr ise different statistical features that can be explained by nondynamic al statistics. For instance, one observes certain lag one serial corre lation functions for consecutive periods during periodic notion. This work aims at an extension of dynamical descriptions in terms of stocha stically forced nonlinear oscillators such as.. xi+omega(0)(2)xi= n(xi ,xi)+q(xi,xi)Psi(t), were the nonlinear function n(xi,xi) generates a limit cycle and Psi(t) denotes colored noise that is multiplied via q( xi,xi). Nonlinear self-excited systems have been frequently investigat ed, particularly emphasizing stability properties and amplitude evolut ion. Thus, one can focus on the effects of noise on the frequency or p hase dynamics that can be analyzed by use of time-dependent Fokker-Pla nck equations. It can be shown that noise multiplied via polynoms of a rbitrary finite order cannot generate the desired period correlation b ut predominantly results in phase diffusion. The system is extended in terms of forced oscillators in order to find a minimal model producin g the required error correction.