R. Diaz-sierra et al., Graph-theoretic description of the interplay between non-linearity and connectivity in biological systems, MATH BIOSCI, 156(1-2), 1999, pp. 229-253
The purpose of this article is to stress the implications that the consider
ation of nonlinearity has upon the extension and strength of connectivity,
if this is understood as a characterization of the degree of interrelation
between parts of the system. This objective is reached within the QP formal
ism for non-linear ODEs. The formalism is developed in a graph-theoretic se
tting, with the help of which the connectionist aspect of non-linearity bec
omes apparent. Topology-preserving transformations involve an exchange betw
een the degree of non-linearity and the strengths of interactions, thus ass
embling systems of apparently different nature into classes of equivalence.
We argue that, if we have in mind a classification of systems according to
behavior, these classes of equivalence should be given their proper singul
arity. We characterize globally the connectivity of a class with an index,
although we point out during the discussion that the mathematical conceptio
n of the complex idea of connectivity is still incomplete. (C) 1999 Elsevie
r Science Inc. All rights reserved.