Lutz Schimansky-Geier

Nonlinear dynamics of chaotic and stochastic systems : tutorial and modern developments

From the contents: Tutorial * Dynamical Systems * Fluctuations in Dynamic Systems * Synchronization of Periodic Systems * Dynamical Chaos * Routes to Chaos * Synchronization of Chaos * Controlling Chaos * Reconstruction of Dynamical Systems * Stochastic Dynamics * Stochastic Resonance * Synchronization of Stochastic Systems * The Beneficial Role of Noise in Excitable Systems * Noise Induced Transport.

Synchronization in ensembles of stochastic resonators

We study the response of a parallel ensemble of stochastic resonators to external signals. For small signals linear response theory is used. We show that for a large number of elements this ensemble can be used to process broadband signals without frequency distortions. Nonlinear effects manifest themselves by the phenomenon of synchronization. Although synchronization is not observed at the output of single elements the mean frequency of the collective response is locked by the input signal. It takes place for a sufficiently large number of elements in a wide range of internal noise intensities. We also show that the synchronization is accompanied by a nonmonotonous Shannon entropy of the collective output indicating noise-induced order.

Why Going Zig‐Zag?

We report a theory to describe the motion of zooplankton. Apart from moving just randomly like a classical Brownian particle, zooplankton like Daphnia or Copepods pick their turning angle from a distribution which is far from being Gaussian or equally distributed. This leads to different behavior in the motion compared to normal diffusion. The question which can be asked here is: Is there an evolutionary reason to forage for food in the aforementioned manner? First attempts to answer the question are made throughout this manuscript although it still remains an unsolved problem.

Spatio-temporal stochastic resonance of a domain wall motion in an inhomogeneous magnet

Abstract We study the motion of a small-angle domain wall (DW) in a rhombic ferromagnet with localized attracting inhomogeneities in the vicinity of the reorientational phase transition induced by temperature. Usually DW can be trapped by the inhomogeneities. If the system is additionally driven by noisy magnetic field the DW is able to perform stochastic motion and hence there is a nonzero probability of DW jumps between several attracting inhomogeneities. With small periodic magnetic field applied to the system we will observe stochastic resonance in the motion of the DW. At an optimal noise level the hopping dynamics of the DW becomes most coherent and the response of the system to the periodic force is maximal.