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DY: Fachverband Dynamik und Statistische Physik

DY 16: Statistical Physics in Biological Systems (joint session DY/ BP)

DY 16.5: Vortrag

Mittwoch, 2. April 2014, 10:45–11:00, ZEU 160

Pattern formation in individual-based systems with time-varying parameters — •Peter Ashcroft and Tobias Galla — The University of Manchester, Manchester, UK

We study the patterns generated in finite-time sweeps across symmetry-breaking bifurcations in individual-based models of evolutionary dynamics and cell differentiation. Similar to the well-known Kibble-Zurek scenario of defect formation, large-scale patterns are generated when model parameters are varied slowly, whereas fast sweeps produce a large number of small domains. The symmetry breaking is triggered by intrinsic noise, originating from the discrete dynamics at the microlevel. Based on a linear-noise approximation, we calculate the characteristic length scale of these patterns. We demonstrate the applicability of this approach in a model of evolutionary game theory with a time-dependent fitness structure, and in a model of cell differentiation, which we relate to Waddington's epigenetic landscape. Our theoretical estimates are confirmed in simulations. In further numerical work, we observe a similar phenomenon when the symmetry-breaking bifurcation is triggered by population growth.

Reference: P. Ashcroft and T. Galla, Phys. Rev. E 88, 062104 (2013)