Self-organization evolution of a population is studied considering generalized reaction-diffusion equations. We proposed a model based on non-local operators that has several of the equations traditionally used in research on population dynamics as particular cases. Then, employing a relatively simple functional form of the non-local kernel, we determined the conditions under which the analyzed population develops spatial patterns, as well as their main characteristics. Finally, we established a relationship between the developed model and real systems by making simulations of bacterial populations subjected to non-homogeneous lighting conditions. Our proposal reproduces some of the experimental results that other approaches considered previously had not been able to obtain.

考虑广义反应扩散方程，研究了种群的自组织演化。我们提出了一个基于非本地算子的模型，该模型具有在特定情况下人口动力学研究中传统上使用的几个方程式。然后，采用非本地内核的相对简单的功能形式，我们确定了所分析种群发展空间格局的条件及其主要特征。最后，我们通过模拟细菌在非均匀光照条件下的种群来建立开发模型与实际系统之间的关系。我们的建议再现了一些以前考虑过的其他方法无法获得的实验结果。