Our Research

Phenomena at the interface between biology and chemistry are at the hearth of our research. Self-Organization and Pattern Formation are prominent features of the biological realm. The complex dynamical systems that we investigate are showing these types of features, nonetheless they are classically seen as not yet alive. Fact is that these systems are part of many organisms and function, for example, as pacemakers or biological clocks. Our research focuses on understanding the complex interactions and processes that take place in these type of complex systems in a wider context. By doing so, we hope to gain a more holistic approach to the phenomena of life. In the following we present our research and describe in detail which phenomena we are focusing on. At the end there is a complete list of all publications, poster contributions and talks carried out by our institute (click here to go there directly).

Appearance of spiral waves in a biological (see: Loose et al., 2008) aswell as in a chemical system (taken from:Philippe Plailly/Science Photo Library)

Transient Chaos in a Chemical Oscillator

Effect of an Limited Stirring Phase on the Transition from Order to Chaos

We discovered that the chaotic phase can be controlled by a limited stirring phase of typical time spans of half an hour to an hour. The effects of stirring on the BZ reaction may have other consequences too apart from the pure homogenization of the system. We have investigated the system under different conditions (changing dimensions and volume of the beaker, different stirring rates and times). We have found that the stirring can result in the complete disappearance of the chaotic phase which is present in the non-stirred case. We expect that the stirring time plays the role of a ‘bifurcation parameter’. Details on this research can be found in the following article. F. Wodlei, M. R. Hristea. Effect of Limited Stirring on the Belousov Zhabotinsky Reaction. Proceedings of the European Conference on Complex Systems 2012 (September 2013)

Effect of limited stirring. top: stirring phase of 60 mins (disapearance of the chaotic phase); middle: stirring phase of 30 mins; no stirring phase.

Periodic Motion in the Chaotic Phase of the Belousov Zhabotinsky Reaction

The convective motion in the unstirred Belousov Zhabotinsky Reaction is highly influencing the chemical reactions. We have recently discovered that, as the so-called chaotic transient takes place, periodic bulk motions in form of convective cells are created in the reaction solution. The behavior of an unstirred BZ reaction in a batch configuration is more complex than it is in constantly stirred tank reactors or in Petri dishes. This is due to the complex coupling between reaction kinetics, convection and diffusion. In both cases either convection and diffusion or convection only is suppressed. Normally, a BZ reaction in a batch configuration is investigated in a spectrophotometer, where possible inhomogeneities or convective motions in the bulk solution cannot be seen. In this work we focused on these inhomogeneities and we investigated the convective motion created in the chaotic phase in an unstirred BZ reaction in a cuvette configuration. The ordered convective cells observed in specific cuvette geometries were investigated in respect to the local chemical kinetics in the reaction solution. Surprisingly, we discovered that this ordered hydrodynamical structures are correlated to the chaotic nature of the local chemical kinetics. As a first explanation of this correlation, we assume that the formed convection cells lead to a “de-synchronization” of the previously homogeneous color oscillations moving the system into a chaotic phase. With the simple mathematical model presented here we were able to indirectly confirm the same qualitative results, i.e. that a connection between chemical chaos and hydrodynamical order in such systems exists. Details on this research can be found in the following article. Florian Wodlei, Mihnea R. Hristea and Giuseppe Alberti: Periodic Motion in the Chaotic Phase of an Unstirred Ferroin-Catalyzed Belousov Zhabotinsky Reactioni>. Front. Chem., 08 July 2022, Sec. Physical Chemistry and Chemical Physics, 10:881691 (2022)

Convection cells in the special cuvette during the chaotic phase. (A–D) show the presence of two convection cells (liquid moves up in the middle and down on the left and right side). Images were obtained by averaging over 60 s, (E) shows the time series extracted from the video data where the red part corresponds to the periodic phase. Arrows indicate the times where the images (A–D) were created (spikes in the time series correspond to the passage of bubbles). Insets show the periodic phase (left) and part of the chaotic phase (right) magnified.

A Symbol Dynamic Approach to Characterize the Chaoticity in the Belousov Zhabotinsky Reaction

Determination of the behavior of a system by analyzing the dynamics of one or more variables characterizing the system over time is a canonical approach in the scientific context. The evaluation of such time series is based on a number of different methods such as the calculation of the Lyapunov-Exponent, the phase space reconstruction by time delay or the Fast Fourier Transform (FFT) and the corresponding power spectrum. Each of these methods have their limitations and create more or less reliable results. For highly complex systems, as, for example, the Belousov Zhabotinsky reaction, conclusive results are difficult to obtain. Neither the transcription of time series into sequences of symbols nor the statistical analysis of these sequences is new. What is new in our approach is that we are not only looking at the topological invariants but also at the detailed distributions of the frequencies of different words that correspond to each times series sequence. This approach allows us to describe the different types of behavior, specifically the chaotic one, in a more accurate way than the above mentioned methods. A first investigation showed that the so-called chaotic phase is indeed a mixture between a chaotic and an order behaviour. Details on this research were presented at the Gordon Research Seminar (GRS) in the summer 2024 (see our poster) and will soon be published.

Frequency distribution of the number of times a certain word is found in the chaotic sequence of the Belousov Zhabotisky reaction in the chaotic phase.