2,610 research outputs found
Pattern formation in individual-based systems with time-varying parameters
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.Comment: 16 pages, 9 figures. Published version. Corrected missing appendix
link from previous versio
Stochastic processes with distributed delays: chemical Langevin equation and linear-noise approximation
We develop a systematic approach to the linear-noise approximation for
stochastic reaction systems with distributed delays. Unlike most existing work
our formalism does not rely on a master equation, instead it is based upon a
dynamical generating functional describing the probability measure over all
possible paths of the dynamics. We derive general expressions for the chemical
Langevin equation for a broad class of non-Markovian systems with distributed
delay. Exemplars of a model of gene regulation with delayed auto-inhibition and
a model of epidemic spread with delayed recovery provide evidence of the
applicability of our results.Comment: 21 pages, 7 figure
Complexity measures, emergence, and multiparticle correlations
We study correlation measures for complex systems. First, we investigate some
recently proposed measures based on information geometry. We show that these
measures can increase under local transformations as well as under discarding
particles, thereby questioning their interpretation as a quantifier for
complexity or correlations. We then propose a refined definition of these
measures, investigate its properties and discuss its numerical evaluation. As
an example, we study coupled logistic maps and study the behavior of the
different measures for that case. Finally, we investigate other local effects
during the coarse graining of the complex system.Comment: 13 pages, 5 figures, accepted by Phys. Rev.
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