A revised model of fluid transport optimization in Physarum polycephalum

TL;DR

This paper proposes a revised model for fluid transport in Physarum polycephalum, suggesting pressure gradient control over flow volume, and demonstrates its stability and broader applicability compared to previous models.

Contribution

It introduces a new hypothesis that pressure gradients, rather than flow volume, control tube adaptation, supported by stability analysis and simulations.

Findings

Revised model supports global flow optimization.

Model stable for a wider class of response functions.

Simulations indicate applicability to arbitrary networks.

Abstract

Optimization of fluid transport in the slime mold Physarum polycephalum has been the subject of several modeling efforts in recent literature. Existing models assume that the tube adaptation mechanism in P. polycephalum's tubular network is controlled by the sheer amount of fluid flow through the tubes. We put forward the hypothesis that the controlling variable may instead be the flow's pressure gradient along the tube. We carry out the stability analysis of such a revised mathematical model for a parallel-edge network, proving that the revised model supports the global flow-optimizing behavior of the slime mold for a substantially wider class of response functions compared to previous models. Simulations also suggest that the same conclusion may be valid for arbitrary network topologies.