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

Article type: Research Article

Authors: Bretti, Gabriella^* | Natalini, Roberto

Affiliations: Istituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle Ricerche, Via dei Taurini, Rome, Italy

Correspondence: [*] Corresponding author: Gabriella Bretti, Istituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle Ricerche, Via dei Taurini, 19 – 00185 Rome, Italy. E-mail: [email protected].

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

DOI: 10.3233/JCM-170773

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 18, no. 1, pp. 85-115, 2018