Right Network-Preserving Diffeomorphisms

Fernando Antoneli and Ian Stewart

Journal of Singularities
volume 25 (2022), 1-29

Received: 21 January 2021. Received in revised form: 7 May 2022.

DOI: 10.5427/jsing.2022.25a

Add a reference to this article to your citeulike library.

Abstract:

In the formal theory of networks of coupled dynamical systems, the topology of the network and a classification of nodes and arrows into specific types determines a class of 'admissible' ODEs that are compatible with the network structure. In dynamical systems theory and singularity theory, coordinate changes that preserve appropriate structures play key roles. Coordinate changes appropriate for network dynamics should, in particular, preserve admissibility. Such 'network-preserving diffeomorphisms' have been characterised completely for fully inhomogeneous networks, and for five types of action: right, left, contact, vector field, and conjugacy. Here we characterise right network-preserving diffeomorphisms for an arbitrary network. Such coordinate changes are, in particular, appropriate for the study of homeostasis, which occurs in a biological or chemical system when some output variable remains approximately constant as input parameters vary over some region.

2000 Mathematical Subject Classification:

Primary 05C20; Secondary 05C25, 20B25

Key words and phrases:

Coupled Systems, Right equivalence, Homeostasis, Perfect Adaptation

Author(s) information:

Fernando Antoneli
Centro de Bioinformática Médica
Universidade Federal de São Paulo
São Paulo SP 04023-062, Brazil

Ian Stewart
Mathematics Institute
University of Warwick
Coventry CV4 7AL, UK