Gorban, A.N. (2004) Systems with inheritance: dynamics of distributions with conservation of support, natural selection and finitedimensional asymptotics. [Preprint]
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Abstract
If we find a representation of an infinitedimensional dynamical system as a nonlinear kinetic system with {\it conservation of supports} of distributions, then (after some additional technical steps) we can state that the asymptotics is finitedimensional. This conservation of support has a {\it quasibiological interpretation, inheritance} (if a gene was not presented initially in a isolated population without mutations, then it cannot appear at later time). These quasibiological models can describe various physical, chemical, and, of course, biological systems. The finitedimensional asymptotic demonstrates effects of {\it ``natural" selection}. The estimations of asymptotic dimension are presented. The support of an individual limit distribution is almost always small. But the union of such supports can be the whole space even for one solution. Possible are such situations: a solution is a finite set of narrow peaks getting in time more and more narrow, moving slower and slower. It is possible that these peaks do not tend to fixed positions, rather they continue moving, and the path covered tends to infinity at $t \rightarrow \infty$. The {\it drift equations} for peaks motion are obtained. Various types of stability are studied. In example, models of cell division selfsynchronization are studied. The appropriate construction of notion of typicalness in infinitedimensional spaces is discussed, and the ``completely thin" sets are introduced.
Item Type:  Preprint 

Keywords:  Selection, Limit sets, Kinetic equations, Selfsynchronization, Finitedimensional asymptotic 
Subjects:  Computer Science > Dynamical Systems 
ID Code:  3815 
Deposited By:  Gorban, Prof Alexander N. 
Deposited On:  09 Sep 2004 
Last Modified:  11 Mar 2011 08:55 
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