Bratus Alexander S, Posvyanskii Vladimir P, Novozhilov Artem S
Moscow State University of Railway Engineering, Moscow, Russia.
Nonlinear Anal Real World Appl. 2010 Jun 1;11(3):1897-1917. doi: 10.1016/j.nonrwa.2009.04.013.
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.
本文对空间扩展的自催化和超循环系统进行了分析。结果表明，具有全局调控的反应扩散方程形式的空间显式系统具有与相应局部模型相同的主要定性特征。特别地，利用引入的平均积分意义下的稳定性概念，我们证明了自催化系统的竞争排斥原理和超循环系统的持久性。研究了稳态解的存在性和稳定性。对于某些参数值，证明了稳定的空间非均匀解的出现。
