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arXiv · 1308.6101

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

Peter Ashcroft·Tobias Galla
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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 micro-level. 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.

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BibTeXRIS

Peter Ashcroft, Tobias Galla. 2013-12-03. Pattern formation in individual-based systems with time-varying parameters. https://doi.org/10.1103/physreve.88.062104

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