Abstract Chemical Organization Theory (COT) has been successfully applied to analyze complex reaction networks where species interact and new species can emerge. The COT has been well studied, but is yet to analyze high dimensional systems dynamics over time equivalent to ordinary differential equations. Moreover, spatial effects, such as diffusion and boundary conditions have also not been considered yet. Here, we extend the COT to cope with reaction-diffusion systems. Thereby we focus on the effects of diffusion and various boundary conditions. In order to demonstrate the effectiveness of our approach, we analyze two models based on partial differential equations, one of which is on HIV virus dynamics. The analysis shows interesting organizational structures when using different ranges of diffusion rates, as well as for Dirichlet and positive Neumann boundary conditions. The advantage of this novel approach is that it is based solely on the model structure (reaction rules) but is independent of kinetic details, such as rate constants. Hence, it copes with high-dimensional systems without the need of numerical simulations, and it can be applied without detailed mathematical knowledge. Our tool is available, without restriction at https://github.com/stephanpeter/orgs-rds .

中文翻译：

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反应扩散系统中的组织：扩散和边界条件的影响

摘要 化学组织理论 (COT) 已成功应用于分析物种相互作用和可能出现新物种的复杂反应网络。COT 已经得到了很好的研究，但还没有分析高维系统动力学随着时间的推移等效于常微分方程。此外，还没有考虑空间效应，例如扩散和边界条件。在这里，我们扩展了 COT 以应对反应扩散系统。因此，我们专注于扩散和各种边界条件的影响。为了证明我们的方法的有效性，我们分析了基于偏微分方程的两个模型，其中之一是关于 HIV 病毒动力学。当使用不同的扩散率范围时，分析显示了有趣的组织结构，以及 Dirichlet 和正 Neumann 边界条件。这种新方法的优点是它完全基于模型结构（反应规则），但与动力学细节无关，例如速率常数。因此，它无需数值模拟即可处理高维系统，无需详细的数学知识即可应用。我们的工具可在 https://github.com/stephanpeter/orgs-rds 不受限制地使用。