Analytical analysis of spatially extended autocatalytic and hypercyclic systems is presented. It is shown that spatially explicit systems in the form of reaction-diffusion equations with global regulation possess the same major qualitative features as the corresponding local models. In particular, using the introduced notion of the stability in the mean integral sense we prove the competitive exclusion principle for the autocatalytic system and the permanence for the hypercycle system. Existence and stability of stationary solutions are studied. For some parameter values it is proved that stable spatially non-uniform solutions appear.

中文翻译：

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全局调节和非线性增长率下空间扩展自催化和超循环系统的固定解的存在性和稳定性。

提出了空间扩展自催化和超循环系统的分析分析。结果表明，具有全局调节的反应扩散方程形式的空间显式系统与相应的局部模型具有相同的主要定性特征。特别是，使用引入的平均积分意义上的稳定性概念，我们证明了自催化系统的竞争排除原理和超循环系统的永久性。研究了平稳解的存在性和稳定性。对于某些参数值，证明出现稳定的空间非均匀解。