Hyperchaos and chemical turbulence in enzymatic reaction‐diffusion systems

Nonlinear dynamic conversion of analog signals into excitation patterns

Local periodic perturbations induce frequency-dependent propagation waves in an excitable spatiotemporally chaotic system. We show how segments of noise-contaminated and chaotic perturbations induce characteristic sequences of excitations in the model system. Using a set of "tuned" excitable systems, it is possible to characterize signals by their spectral composition of excitation pattern. As an example, we analyze an epileptic "spike-and-wave" time series.

Human electroencephalogram induces transient coherence in excitable spatiotemporal chaos

A time series from a human electroencephalogram (EEG) is used as a local perturbation to a reaction-diffusion model with spatiotemporal chaos. For certain finite ranges of amplitude and frequency it is observed that the strongly irregular perturbations can induce transient coherence in the chaotic system. This could be interpreted as "on-line" detection of an inherently correlated pattern embedded in the EEG.

Complex patterns predicted in an in vitro experimental model system for the evolution of molecular cooperation

An isothermal biochemical in vitro amplification system with two trans-cooperatively coupled amplifying DNA molecules was investigated homogeneously using a hierarchy of kinetic models and as a simplified reaction-diffusion system. In our model of this recently developed experimental system, no reaction mechanism higher than second order occurs, yet numerical simulations show a variety of complex spatiotemporal patterns which arise in response to finite amplitude perturbations in a flow reactor. In a certain domain of the kinetic parameters the system shows self-replicating spots. These spots can stabilize the cooperative amplification in such evolving systems against emerging parasites. The results are of high relevance for experimental studies on these functional in vitro ecosystems in spatially resolved microstructured reactors.