Convergence Properties for the Physarum Solver
  The Physarum solver is an intuitive mechanism for solving optimisation problems based on the idea of an electrical network, whereby the conductivity is reinforced by the current. We show that the Physarum solver obtains the solution to the linear transshipment problem on a digraph and that the electrical potential converges to an infinity-harmonic solution of the dual problem. 
Kentaro Ito and Anders Johansson and Toshiyuki Nakagaki and Atsushi   Tero
math.OC math.CO math.DS