Pattern formation in individual-based systems with time-varying parameters

Authored by Tobias Galla, Peter Ashcroft

Date Published: 2013

DOI: 10.1103/physreve.88.062104

Sponsors: United Kingdom Engineering and Physical Sciences Research Council (EPSRC)

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

We study the patterns generated in finite-time sweeps across symmetry-breaking bifurcations in individual-based models. 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 simple model of opinion dynamics, a model in evolutionary game theory with a time-dependent fitness structure, and a model of cell differentiation. 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.

Tags

Simulation Transitions Dynamics Populations Defect formation String formation Vortex formation Symmetry breaks Superfluid he-3 Liquid-crystals