A new model to imitate the foraging behavior of Physarum polycephalum on a nutrient-poor substrate

Researches on Physarum polycephalum show that methods inspired by the primitive unicellular organism can construct an efficient network and solve some complex problems in graph theory. Current models simulating the intelligent behavior of Physarum are mainly based on Hagen-Poiseuille Law and Kirchhoff Law, reaction-diffusion, Cellular Automaton and multi-agent approach. In this paper, based on an assumption that the plasmodium of Physarum forages for food along the gradient of chemo-attractants on a nutrient-poor substrate, a new model is proposed to imitate its intelligent foraging behavior. The key point of the model is that the growth of Physarum is determined by the simple particle concentration field relating the distance to food source and the shape of food source on a nutrient-poor substrate. To verify this model, numerical experiments are conducted according to Adamatzky׳s experiment. Results in spanning tree construction by this model are almost the same as those of Physarum and Oregonator model. The proposed model can also imitate Physarum to avoid repellents. Furthermore, the Euclidean Spanning tree built by this model is similar to its corresponding Minimal Euclidean Spanning tree.