Graph-theoretic description of the interplay between non-linearity and connectivity in biological systems
type: Item
instance of: scholarly article
title: Graph-theoretic description of the interplay between non-linearity and connectivity in biological systems
zbMATH Open document ID: 0954.92001
DOI: 10.1016/S0025-5564(98)10068-8
author: R. Diaz-Sierra
author: Benito Hernández-Bermejo
author: V. Fairén
published in: Mathematical Biosciences
publication date: 2001-02-14T00:00:00Z
review text: The main idea of the present study refers to the reconsideration of connectivity, a concept that should be discussed versus linear differential systems. Also, the idea of a class of equivalences of systems characterized of the same behaviour reveals the possible connectivity - behavior relation. The suggestions proposed refer to the definition of an index of the class. Stress is also laid on the implications of nonlinarity on connectivity (extension and strength), as based on the application of the \(QP\)-formalism to nonlinear ODEs. The connectionist representations considered in this study belong to biological systems, viewed as a set of elementary units which form together a network. The main generic qualitative features, e.g., the amount, distribution, and sign of internal connections, are essential notions in the demonstration made by the authors. They show that the realization of a mathematical scheme capable of agreeing with a connectionist point of view is possible. A connectionist representation involves a graph made of nodes (vertices) and connections (links, edges or arcs) between them. To conclude with, the study provides a connectionist description of \(QP\) systems, based on a graph-theoretical representation, which supports the idea of a deep interplay between nonlinearity and connectivity.
Mathematics Subject Classification ID: 92B05
Mathematics Subject Classification ID: 05C90
zbMATH DE Number: 1359707
zbMATH Keywords: nonlinearity
zbMATH Keywords: extension stress
zbMATH Keywords: QP systems
zbMATH Keywords: QP formalisms
zbMATH Keywords: connectivity
Wikidata QID: Q52217763
reviewed by: Cristina Irimia
describes a project that uses: MACSYMA
MaRDI profile type: Publication
cites work: Q3992992
cites work: Dynamics of small autocatalytic reaction networks. I: Bifurcations, permanence and exclusion
cites work: DISCUSSION PAPER: THE QUALITATIVE ANALYSIS OF PARTIALLY SPECIFIED SYSTEMS
cites work: Global stability of ecosystems of the generalized Volterra type
cites work: Lotka-Volterra equation and replicator dynamics: A two-dimensional classification
cites work: Random ecological systems with structure: Stability-complexity relationship
cites work: Q3696908
cites work: Q3994902
cites work: Nonpolynomial vector fields under the Lotka-Volterra normal form
cites work: Lotka-Volterra representation of general nonlinear systems
cites work: Algebraic recasting of nonlinear systems of ODEs into universal formats
cites work: Investigation of Painlevé property under time singularities transformations
cites work: Indirect effects in ecological interaction networks. I: The chain rule approach
cites work: Q4003916
full work available at URL: s0025-5564(98)10068-8
OpenAlex ID: W2072520670
description: scientific article; zbMATH DE number 1359707