标题： 非局部种群动力学的模式形成和共存区域 显示英文标题

标题： Pattern formation and coexistence domains for a nonlocal population dynamics

摘要： 在本次交流中，我们提出一个最一般的方程，用于研究单物种种群的模式形成及其在长度为L的系统中的极限区域。为了实现这一点，我们在生长和竞争项中引入了非局部性，其中积分核现在依赖于特征长度参数alpha和beta。 因此，我们推导出一个参数空间 (alpha,beta) ，在此空间中可以分析共存曲线 alpha*=alpha*(\beta ) ，该曲线限定了种群动力学系统中模式形成（或不存在）的区域。 我们表明，这条曲线与经典热力学和临界现象物理中的共存曲线有相似之处。 我们成功地将该模型与大肠杆菌种群扩散的实验数据进行了比较。 显示英文摘要

摘要： In this communication we propose a most general equation to study pattern formation for one-species population and their limit domains in systems of length L. To accomplish this we include non-locality in the growth and competition terms where the integral kernels are now depend on characteristic length parameters alpha and beta. Therefore, we derived a parameter space (alpha,beta) where it is possible to analyze a coexistence curve alpha*=alpha*(\beta) which delimits domains for the existence (or not) of pattern formation in population dynamics systems. We show that this curve has an analogy with coexistence curve in classical thermodynamics and critical phenomena physics. We have successfully compared this model with experimental data for diffusion of Escherichia coli populations.