Synchronisation of time--delay systems

We present the linear-stability analysis of synchronised states in coupled time-delay systems. There exists a synchronisation threshold, for which we derive upper bounds, which does not depend on the delay time. We prove that at least for scalar time-delay systems synchronisation is achieved by transmitting a single scalar signal, even if the synchronised solution is given by a high-dimensional chaotic state with a large number of positive Lyapunov-exponents. The analytical results are compared with numerical simulations of two coupled Mackey-Glass equations

A three-species model explaining cyclic dominance of pacific salmon

The four-year oscillations of the number of spawning sockeye salmon (Oncorhynchus nerka) that return to their native stream within the Fraser River basin in Canada are a striking example of population oscillations. The period of the oscillation corresponds to the dominant generation time of these fish. Various - not fully convincing - explanations for these oscillations have been proposed, including stochastic influences, depensatory fishing, or genetic effects. Here, we show that the oscillations can be explained as a stable dynamical attractor of the population dynamics, resulting from a strong resonance near a Neimark Sacker bifurcation. This explains not only the long-term persistence of these oscillations, but also reproduces correctly the empirical sequence of salmon abundance within one period of the oscillations. Furthermore, it explains the observation that these oscillations occur only in sockeye stocks originating from large oligotrophic lakes, and that they are usually not observed in salmon species that have a longer generation time.Comment: 7 pages, 5 figure

Stochastic Resonance in Chaotic Spin-Wave Dynamics

We report the first experimental observation of noise-free stochastic resonance by utilizing the intrinsic chaotic dynamics of the system. To this end we have investigated the effect of an external periodic modulation on intermittent signals observed by high power ferromagnetic resonance in yttrium iron garnet spheres. Both the signal-to-noise ratio and the residence time distributions show the characteristic features of stochastic resonance. The phenomena can be explained by means of a one-dimensional intermittent map. We present analytical results as well as computer simulations.Comment: 4 pages, revtex, 5 eps figures included, also available "via www http://athene.fkp.physik.th-darmstadt.de/public/wolfram.html" or "via ftp ftp://athene.fkp.physik.th-darmstadt.de/pub/publications/wolfram/", Phys. Rev. Lett. in pres

On the Collective Motion in Globally Coupled Chaotic Systems

A mean-field formulation is used to investigate the bifurcation diagram for globally coupled tent maps by means of an analytical approach. It is shown that the period doubling sequence of the single site map induces a continuous family of periodic states in the coupled system. This type of collective motion breaks the ergodicity of the coupled map lattice. The stability analysis suggests that these states are stable for weak coupling strength but opens the possibility for more complicated types of motion in the regime of moderate coupling.Comment: 12 pages, Latex, 3 eps figures included also available "at http://athene.fkp.physik.th-darmstadt.de/public/wolfram.html" or "at ftp://athene.fkp.physik.th-darmstadt.de/pub/publications/wolfram/" Phys. Rep. in pres