A. Daffertshofer, EFFECTS OF NOISE ON THE PHASE DYNAMICS OF NONLINEAR OSCILLATORS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 58(1), 1998, pp. 327-338
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.