title: Graph-theoretic description of the interplay between non-linearity and connectivity in biological systems.
abstract: The purpose of this article is to stress the implications that the consideration 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 formalism for non-linear ODEs. The formalism is developed in a graph-theoretic setting, with the help of which the connectionist aspect of non-linearity becomes apparent. Topology-preserving transformations involve an exchange between the degree of non-linearity and the strengths of interactions, thus assembling 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 singularity. We characterize globally the connectivity of a class with an index, although we point out during the discussion that the mathematical conception of the complex idea of connectivity is still incomplete.
authors: Departamento de Física Fundamental, Universidad Nacional de Educación a Distancia, Madrid, Spain. sierra@apphys.uned.es
authors: R
authors: R
authors: Díaz-Sierra
authors: B
authors: B
authors: Hernández-Bermejo
authors: V
authors: V
authors: Fairén
mesh_terms: D016014:Linear Models; D008954:Models, Biological; D016571:Neural Networks, Computer