Stationary and dynamic solutions of stochastic relaxation oscillators

Two different approaches are proposed to obtain explicit solutions for stochastic relaxation oscillator problems in the weak noise limit. The first method generalizes the idea of the cumulant expansion. It does not presuppose an analytical treatment of the deterministic motion. It is however restricted to the discussion of stationary situations. In the second method an adiabatic elimination of irrelevant variables allows for the computation of time dependent solutions. It can be carried through only if the deterministic limit cycle is known analytically. As special examples the stationary solutions of the stochastic van der Pol oscillator and time dependent solutions of a simple one dimensional model system have been obtained.This article is an excerpt from a dissertation presented at TH Darmstadt, Darmstädter Dissertation D17This work was performed within a program of the Sonderforschungsbereich 185 Darmstadt-Frankfurt, FRG     

Analytical treatment of fluctuation spectra at the symmetry breaking chaos transition

The phase transition of characteristic exponents describing the fluctuations of temporal coarse grained quantities is investigated for the symmetry breaking bifurcation. The discussion of the eigenvalues of the transfer operator clarifies the origin of the phase transition and leads to scaling relations in the vicinity of the bifurcation point.     

Alkaloids from Croton flavens L. and their affinities to GABA-receptors

Phytochemical investigation of several plants of Croton flavens L. from Barbados has led to the isolation of the tetrahydroprotoberberine alkaloids scoulerine and coreximine, as well as the morphinanedienones salutaridine and its racemic form salutarine, sebiferine, norsinoacutine and flavinantine. In a screening for 3H-GABA displacing activity coreximine showed the highest affinity to the GABA(A) receptor.     

Theoretical and experimental aspects of chaos control by time-delayed feedback

We review recent developments for the control of chaos by time-delayed feedback methods. While such methods are easily applied even in quite complex experimental context the theoretical analysis yields infinite-dimensional differential-difference systems which are hard to tackle. The essential ideas for a general theoretical approach are sketched and the results are compared to electronic circuits and to high power ferromagnetic resonance experiments. Our results show that the control performance can be understood on the basis of experimentally accessible quantities without resort to any model for the internal dynamics.