Slime mould (Physarum) may not have brains, but they are capable of solving many significant and challenging problems. Existing models for studying the intelligent behaviour of Physarum have overlooked its foraging behaviour under competitive settings. In this research, we propose a new model based on Cellular Automata (CA) and Reaction Diffusion (RD) system, where multiple Physarum interact with each other and with their environment. The novelty of our model is that the Physarum has six neighbours at equidistant (hexagonal CA), furthermore, we have extended the model to 3D and multi-dimensional CA grid. The growth of Physarum is determined by the balance between attraction force towards food resources (determined by mass and quality) and repulsion forces between competing Physarum according to their power (mass) and hunger motivation. To validate this model, numerical experiments were conducted. Physarum with more mass succeeded in engulfing a larger number of food resources with high quality in shorter time (number of iteration). It also occupied larger area of the grid (territory) and excluded its competitors. We also conducted empirical analysis to compare the time complexity between the hexagonal and Moore neighbourhood, and it showed that hexagonal neighbourhood is more efficient than Moore in terms of computational cost. To the best of our knowledge, we are the first to present Physarum in competition mathematical model and the algorithms inspired from such a model has demonstrated its promising performance in solving several real world problems such as mobile wireless sensor networks, and discrete multi objective optimization problems.

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