Graph-theoretic description of the interplay between non-linearity and connectivity in biological systems
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.
scientific article; zbMATH DE number 1359707