  In recent years, research on Physarum polycephalum has become more popular
after Nakagaki et al. (2000) performed their famous experiment showing that
Physarum was able to find the shortest route through a maze. Subsequent
researches have confirmed the ability of Physarum-inspired algorithms to solve
a wide range of NP-hard problems. In contrast to previous reviews that either
focus on biological aspects or bio-inspired applications, here we present a
comprehensive review that highlights recent Physarum polycephalum biological
aspects, mathematical models, and Physarum bio-inspired algorithms and their
applications. The novelty of this review stems from our exploration of Physarum
intelligent behaviour in competition settings. Further, we have presented our
new model to simulate Physarum in competition, where multiple Physarum interact
with each other and with their environments. The bio-inspired Physarum in
competition algorithms proved to have great potentials for future research.
