Weak noise approach to the logistic map

Using a nonperturbative weak noise approach we investigate the interference of noise and chaos in simple 1D maps. We replace the noise-driven 1D map by an area-preserving 2D map modelling the Poincare sections of a conserved dynamical system with unbounded energy manifolds. We analyze the properties of the 2D map and draw conclusions concerning the interference of noise on the nonlinear time evolution. We apply this technique to the standard period-doubling sequence in the logistic map. From the 2D area-preserving analogue we, in addition to the usual period-doubling sequence, obtain a series of period doubled cycles which are elliptic in nature. These cycles are spinning off the real axis at parameters values corresponding to the standard period doubling events.Comment: 22 pages in revtex and 8 figures in ep

Self-replication, Evolvability and Asynchronicity in Stochastic Worlds

Peer reviewe

Fibre‐optic sensing: past reflections and future prospects

This chapter reflects upon the past and on the achievements that fibre sensors have made over the past half-century. It explains the simple observation that market presence of fibre-optic sensing is modest at best. The chapter illustrates the essentials of a photonic system. Photonics as a discipline is most certainly arousing strategic interest with targeted research and development programmes emerging in both the United States and the European Union. The microstructured fibres, also known as photonic crystal fibres, dramatically increased the variety of geometries and optical responses available to fibre-based sensing. These fibres have arrays of wavelength-scale air holes in their transverse cross section, which extend along the full fibre length and define the waveguide properties. Fibre-optic sensing will continue to provide not only exciting research opportunities but also intriguing (and profitable) application niches in the future