Graph-theoretic description of the interplay between non-linearity and connectivity in biological systems

Citation
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
Citations number
33
Categorie Soggetti
Multidisciplinary
Journal title
MATHEMATICAL BIOSCIENCES
ISSN journal
00255564 → ACNP
Volume
156
Issue
1-2
Year of publication
1999
Pages
229 - 253
Database
ISI
SICI code
0025-5564(19990301)156:1-2<229:GDOTIB>2.0.ZU;2-6
Abstract
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.