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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...
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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