See Networks miniproject (inoverleaf), pdf here: Spatial network optimization with a model of the physarum polycephalum or here

Analytical properties of physarum solver

http://epubs.siam.org/doi/pdf/10.1137/1.9781611974331.ch131

Convergence properties of physarum solver

Physarum Can Compute Shortest Paths

PHYSARUM CAN COMPUTE SHORTEST PATHS: A SHORT PROOF

Physarum Can Compute Shortest Paths

IRLS and Slime Mold: Equivalence and Convergence

On a Natural Dynamics for Linear Programming

Tero's model

A mathematical model for adaptive transport network in path findingby true slime mold

A Mathematical Study ofPhysarum polycephalum

http://www.ncbi.nlm.nih.gov/pubmed/18415133

Other models

An Improved Physarum polycephalum Algorithm for the Shortest Path Problem

Physarum Learner: A bio-inspired way of learning structure from data

An adaptive amoeba algorithm for constrained shortest paths

Dynamics

Physarum polycephalum Percolation as a Paradigm for Topological Phase Transitions in Transportation Networks

Experiments

Plasmodial vein networks of the slime mold Physarum polycephalum form regular graphs

Are motorways rational from slime mould's point of view?

Rules for Biologically Inspired Adaptive Network Design

http://www.nature.com/articles/srep03495