We study the patterns generated in finite-time sweeps acrosssymmetry-breaking bifurcations in individual-based models. Similar to thewell-known Kibble-Zurek scenario of defect formation, large-scale patterns aregenerated when model parameters are varied slowly, whereas fast sweeps producea large number of small domains. The symmetry breaking is triggered byintrinsic noise, originating from the discrete dynamics at the micro-level.Based on a linear-noise approximation, we calculate the characteristic lengthscale of these patterns. We demonstrate the applicability of this approach in asimple model of opinion dynamics, a model in evolutionary game theory with atime-dependent fitness structure, and a model of cell differentiation. Ourtheoretical estimates are confirmed in simulations. In further numerical work,we observe a similar phenomenon when the symmetry-breaking bifurcation istriggered by population growth.
展开▼
