Modeling pattern formation with Boltzmann-like equation
نویسندگان
چکیده
We apply a single Boltzmann-like integro-diierential equation to model pattern formation in aspect space. Dynamics of density distributions are considered in two cases. First, the distribution of organisms on the real line is investigated. A linear stability analysis reveals conditions on interactions between the organisms that lead to aggregation and periodic patterns. Use of diiusion approximation and numerical results demonstrate that in limiting semi-deterministic cases peak-like distributions evolve. Second, we model dynamics of dominance distribution in a bumble bee colony. The corresponding numerical results are compared with experimantal observations.
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