We study spreading phenomena in a two-component reaction-diffusion system, modeling the Neolithic transition from hunter-gatherer societies to agricultural societies in Europe. When farmer populations were introduced into the region inhabited by hunter-gatherer populations, farmer populations spread as an expanding wave through Europe. The speed of the wave is observed to tend to be a constant. We analytically compute the spreading velocity of the model, and characterize the longtime behavior of solutions of the model. Without comparison principle, we introduce a new technique that can locate the spreading front in reaction-diffusion systems.

中文翻译：

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欧洲新石器时代过渡时期农民和猎人-采集者模型的传播速度

我们研究了一个由两部分组成的反应扩散系统的扩散现象，模拟了新石器时代从猎人-采集者社会到欧洲农业社会的过渡。当农民人口被引入到狩猎和采集人口居住的地区时，农民人口就以不断扩大的浪潮在欧洲传播。观察到波速趋于恒定。我们分析计算模型的扩展速度，并表征模型解的长期行为。在没有比较原理的情况下，我们引入了一种新技术，该技术可以确定反应扩散系统中的扩散前沿。