A minimalist model for coevolving supply and drainage networks

Shashank Kumar Anand, Milad Hooshyar, Jan Martin Nordbotten, Amilcare Porporato

Research output: Contribution to journalArticlepeer-review


Numerous complex systems, both natural and artificial, are characterized by the presence of intertwined supply and/or drainage networks. Here, we present a minimalist model of such coevolving networks in a spatially continuous domain, where the obtained networks can be interpreted as a part of either the counter-flowing drainage or co-flowing supply and drainage mechanisms. The model consists of three coupled, nonlinear partial differential equations that describe spatial density patterns of input and output materials by modifying a mediating scalar field, on which supply and drainage networks are carved. In the two-dimensional case, the scalar field can be viewed as the elevation of a hypothetical landscape, of which supply and drainage networks are ridges and valleys, respectively. In the three-dimensional case, the scalar field serves the role of a chemical signal, according to which vascularization of the supply and drainage networks occurs above a critical 'erosion' strength. The steady-state solutions are presented as a function of non-dimensional channelization indices for both materials. The spatial patterns of the emerging networks are classified within the branched and congested extreme regimes, within which the resulting networks are characterized based on the absolute as well as the relative values of two non-dimensional indices.

Original languageEnglish (US)
Article number201407
JournalRoyal Society Open Science
Issue number2
StatePublished - Feb 2021

All Science Journal Classification (ASJC) codes

  • General


  • coupled networks
  • nonlinearity
  • optimal transport


Dive into the research topics of 'A minimalist model for coevolving supply and drainage networks'. Together they form a unique fingerprint.

Cite this