Friday, 27th November 2020

Online Symposium

For information on how to access the event, please contact Henning Reinken via: henning.reinken(at)itp.tu-berlin.de

Guests are welcome!

Differential equations arising from chemical reactions

Prof. Dr. Josef Hofbauer (Universität Wien)

With mass action kinetics, every chemical reaction network can be translated into a polynomial system of ODEs. This results in a rich class of dynamical systems, including gradient systems, oscillating systems, etc. In this survey talk I will also present old and new results about the (global) stability of detailed and complex balanced equilibria.

Topological braiding of vortices in the membrane of a living cell

Dr. Jan F. Totz (Departments of Mathematics and Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, USA)

Braiding of topological structures in complex matter fields provides a robust framework for encoding and processing information, and has been extensively studied in the context of topological quantum computation. In contrast, braiding of topological defects in macroscopic living systems remains to be explored thoroughly.
To this end, we investigate spiral wave turbulence of self-organized Rho-GTP protein waves on the membrane of starfish egg cells. The worldlines of the spiral wave defects undergo rich spontaneous braiding dynamics, and are also capable of forming intricate loop structures. The worldline creation and annihilation events, topological entropy and braiding exponents, as well as loop statistics correlate with cellular activity and exhibit universal scaling behaviors, in agreement with predictions from a generic complex Ginzburg-Landau continuum theory.

Equivariant Pyragas Control on Networks of Relaxation Oscillators

Dr. Isabelle Schneider (Institut für Mathematik, Freie Universität Berlin)

Temporal patterns which also possess spatial components have been neglected so far from the perspective of Pyragas control. In the present talk, we generalize Pyragas control and address pattern-selective control of spatio-temporal patterns in symmetric dynamical systems. This allows us to explicitly target, select and stabilize synchronization patterns. Building on the mathematical foundations developed in the last few years, we now put the theory to test in real experiment. Our principal example is a ring-network of six coupled relaxation oscillators, realized by the Belousov-Zhabotinsky (BZ) reaction. This is joint work with David Hering, Lara Greten, and Jan Totz.