# Selection theorem for systems with inheritance

MATHEMATICAL MODELLING OF NATURAL PHENOMENA（2007）

摘要

The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are apparent in many areas of biology, physics (the theory of parametric wave interaction), chemistry and economics. This conservation of support has a biological interpretation: inheritance. The finite-dimensional asymptotics demonstrates effects of "natural" selection. Estimations of the asymptotic dimension are presented. After some initial time,solution of a kinetic equation with conservation of support becomes a finite set of narrow peaks that become increasingly narrow overtime and move increasingly slowly. It is possible that these peaks do not tend to fixed positions, and the path covered tends to infinity as t ->infinity. The drift equations for peak motion are obtained. Various types of distribution stability are studied:internal stability (stability with respect to perturbations that do not extend the support),external stability or uninvadability (stability with respect to strongly small perturbations that extend the support), and stable realizability (stability with respect to small shifts and extensions of the density peaks). Models of self-synchronization of cell division are studied, as an example of selection in systems with additional symmetry. Appropriate construction of the notion of typicalness in infinite-dimensional space is discussed, and the notion of "completely thin" sets is introduced.

更多查看译文

关键词

dynamics,attractor,dimension,evolution,entropy,natural selection

AI 理解论文

溯源树

样例

生成溯源树，研究论文发展脉络

数据免责声明

页面数据均来自互联网公开来源、合作出版商和通过AI技术自动分析结果，我们不对页面数据的有效性、准确性、正确性、可靠性、完整性和及时性做出任何承诺和保证。若有疑问，可以通过电子邮件方式联系我们：report@aminer.cn