The main goal of this paper is to adapt a class of complexity reduction methods called aggregation of variables methods to the construction of reduced models of two-time reaction-diffusion-chemotaxis models of spatially structured populations and to provide an error bound of the approximate dynamics. Aggregation of variables methods are general techniques that allow reducing the dimension of a mathematical dynamical system. Here we reduce a system of Partial Differential Equations to a simpler Ordinary Differential Equation system, provided that the evolution processes occur at two different time scales: a slow one for the demography and a fast one for migrations and chemotaxis, with a ratio $ \varepsilon>0 $ small enough. We give an approximation of the error between solutions of both original and reduced model for a generic function representing the demography. Finally, we provide an optimization of the error bound and validate numerically this result for a spatial inter-specific model with constant diffusion and population growth given by a logistic law in population dynamics.

中文翻译：

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变量聚合法在一类恒定扩散空间结构种群的二次反应-扩散-趋化模型中的应用

本文的主要目标是适应一类称为变量聚合方法的复杂度降低方法构建空间结构种群的二次反应-扩散-趋化模型的简化模型，并提供近似动力学的误差界限。变量聚合方法是允许减少数学动力系统维数的通用技术。在这里，我们将偏微分方程系统简化为更简单的常微分方程系统，前提是进化过程发生在两个不同的时间尺度上：一个慢的用于人口统计学，一个快速的用于迁移和趋化，比率为 $ \varepsilon >0 $ 足够小。我们给出了代表人口统计的通用函数的原始模型和简化模型的解之间的误差的近似值。最后，