Member # 1
posted 26. July 2002 13:04
DISCRETE DYNAMICS IN NATURE AND SOCIETY 7 (1): 23-26 FEB 2002
A dynamic system interpretation of irreducible complexity
by Boyarsky A, Gora P
Abstract: Behe recently defined the idea of irreducible complexity for biological systems. Using the language of mathematics, we reinterpret his definition from a dynamical systems perspective. Our basic premise is that living
organisms behave dynamically in a chaotic way while predictable periodic behavior reflects cessation of function. We consider the dynamics of a functioning system and altered versions of it to draw conclusions about the irreducible complexity of the original system. The dynamics of an organism is described by means of a discrete time transformation tau on the phase space of the system. The statistical behavior of tau is studied by means of its Frobenius-Perron operator which, in special cases, can be represented by a matrix. Using these matrices we rewrite our definition of irreducible complexity: M is irreducibly complex if it is primitive but no principal submatrix of M is primitive. The primitivity property implies chaotic behavior, while failure to have the primitivity property reflects periodic behavior. Examples of irreducibly complex dynamical systems are presented. We show that certain dynamical systems which are irreducibly complex have an additional property, namely that other systems arbitrarily close to it behave in a dramatically different way. Such behavior suggests that selective evolution by means of small perturbations may not be a general mechanism for achieving the dynamical behavior of a complex system.
[ 26 July 2002, 13:05: Message edited by: Moderator ]