Variational Principle for Self-replicating Systems

Lobachevsky State University of Nizhni Novgorod

^⋆ Corresponding author. E-mail: kuzenkovo@mail.ru

Abstract

The biological theory of natural selection is the key idea for understanding optimality in biology. Selection processes are the base of variational principles in modern biological theory. Biological variational principles are most justified when they are the consequence of selection processes. But the use of the variational principles for explaining strategies of behavior of living species is a difficult problem. In this paper, an order of preference is introduced on the set of hereditary strategies of behavior in general self-replicating systems as a result of selection.

The introduced order of preference is expressed with the help of the comparison criterion, which is an optimality criterion in self-replicating systems. The comparison is made between all kinds of continuous functions of behavior rather than between some discrete collections of variations. Maximization of this criterion is a variational principle in general self-replicating systems.

The newly introduced selection criterion has a series of peculiarities, which are analyzed in this article. One of them is the outcome dependence on initial conditions; in particular the criterion value does not satisfy transitivity while changing the initial conditions. The second feature is the result of the velocity dependence of transients during adaptation. Besides, sometimes the best strategy from the standpoint of the criterion can lead to the system extinction. Methods of accounting of these peculiarities are proposed for optimization of self-replicating systems.