Numerical approximation of nonhomogeneous boundary conditions on networks for a hyperbolic system of chemotaxis modeling the Physarum dynamics

Abstract

Many studies have shown that Physarum polycephalum slime mold is able to find the shortest path in a maze. In this paper we study this behavior in a network, using a hyperbolic model of chemotaxis. Suitable transmission and boundary conditions at each node are considered to mimic the behavior of such an organism in the feeding process. Several numerical tests are presented for special network geometries to show the qualitative agreement between our model and the observed behavior of the mold.

Keywords

Chemotaxis networks finite difference schemes shortest path problem Physarum polycephalum hyperbolic equations AMS subject classification: 92C17 92C42 65M06 05C38 05C85

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