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Selection Theorem for Systems with Inheritance

A. N. Gorban — 2010

Mathematical Modelling of Natural Phenomena

The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with 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: . The finite-dimensional asymptotics demonstrates effects of . Estimations of the asymptotic dimension are...

General Laws of Adaptation to Environmental Factors: from Ecological Stress to Financial Crisis

A. N. GorbanE. V. SmirnovaT. A. Tyukina — 2009

Mathematical Modelling of Natural Phenomena

We study ensembles of similar systems under load of environmental factors. The phenomenon of adaptation has similar properties for systems of different nature. Typically, when the load increases above some threshold, then the adapting systems become more different (variance increases), but the correlation increases too. If the stress continues to increase then the second threshold appears: the correlation achieves maximal value, and start to decrease, but the variance continue to increase. In many...

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