Geodesic
Right Network-Preserving Diffeomorphisms
Journal of Singularities, Tome 25 (2022), pp. 1-29

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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.
DOI : 10.5427/jsing.2022.25a
Classification : 05C20, 05C25, 20B25 
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Fernando Antoneli; Ian Stewart. Right Network-Preserving Diffeomorphisms. Journal of Singularities, Tome 25 (2022), pp. 1-29. doi: 10.5427/jsing.2022.25a

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