September 24, 2020
From ecological systems it is known that events like the extinction of an entire population can come as a surprise, so that countermeasures are late. These phenomena call for explanations, in order to create a deeper understanding of their causes. What are the conditions for maintaining biodiversity as a stable state if even a relatively small fluctuation in the population size can suddenly shift the whole system into another dynamical regime, in which, for example, the diversity is drastically reduced? Fluctuations that have such a drastic effect are rare, but not too rare to actually occur.
Behind the occurrence of such tipping points and states, which are seemingly stable but actually not stable (but only metastable), are often heteroclinic connections. They let the system evolve from one metastable to the next metastable state. Under certain conditions, these connections can form entire networks. These networks are the topic of the research project newly funded by the German Research Foundation (DFG) in the group of Hildegard Meyer-Ortmanns, professor of physics at Jacobs University. The project is financed with about 200,000 euros.
Heteroclinic networks are rather abstract objects from the field of nonlinear dynamics. Exactly because they are sufficiently abstract, they are suited for describing phenomena from very different fields of application. As single connections, they can mediate the rare events just mentioned, when stochastic fluctuations cause the system to tilt towards a completely different dynamical state. As sequences of heteroclinic connections, they provide an effective description of cognitive dynamics in the brain, for example of processes such as the division of a long sequence of numbers into small packages in order to facilitate their memorizing.
If the heteroclinic sequences form a whole cycle, they can manifest themselves in regular oscillations in time or spiral patterns in space. For example, such cycles are realized in lab experiments through Escherichia coli bacteria or in living organisms through an antibiotic-mediated antagonism in bacteria. Presumably, heteroclinic cycles control also different gaits in animals and humans.
Finally, when heteroclinic cycles join together to form entire heteroclinic networks, they may allow for an effective description of dynamic processes in the brain, which are known to run in parallel and interact with each other on the one hand, and on the other hand may be individually organized as a hierarchical structure.
The research group of Professor Meyer-Ortmanns is particularly interested in emergent effects resulting from the coupling of such heteroclinic networks, which in turn influence the control and reproducibility of sequences of metastable states. "Based on our previous experience, we expect a variety of possible synchronization patterns between individual trajectories," says Meyer-Ortmanns. Other applications will quantify the risk of unlikely events which would have drastic consequences for the respective system if they are realized via heteroclinic switches.
Questions are answered by:
Dr. Hildegard Meyer-Ortmanns, Professor of Physics
E-Mail: h.ortmanns [at] jacobs-university.de
Tel: +49 421 200-3221