Chaos–order transition in foraging behavior of ants

Significance We have studied the foraging behavior of group animals that live in fixed colonies (especially ants) as an important problem in ecology. Building on former findings on deterministic chaotic activities of single ants, we uncovered that the transition from chaotic to periodic regimes results from an optimization scheme of the self-organization of such an animal colony. We found that an effective foraging of ants mainly depends on their nest as well as their physical abilities and knowledge due to experience. As an important outcome, the foraging behavior of ants is not represented by random, but rather by deterministic walks, in a random environment: Ants use their intelligence and experience to navigate. The study of the foraging behavior of group animals (especially ants) is of practical ecological importance, but it also contributes to the development of widely applicable optimization problem-solving techniques. Biologists have discovered that single ants exhibit low-dimensional deterministic-chaotic activities. However, the influences of the nest, ants’ physical abilities, and ants’ knowledge (or experience) on foraging behavior have received relatively little attention in studies of the collective behavior of ants. This paper provides new insights into basic mechanisms of effective foraging for social insects or group animals that have a home. We propose that the whole foraging process of ants is controlled by three successive strategies: hunting, homing, and path building. A mathematical model is developed to study this complex scheme. We show that the transition from chaotic to periodic regimes observed in our model results from an optimization scheme for group animals with a home. According to our investigation, the behavior of such insects is not represented by random but rather deterministic walks (as generated by deterministic dynamical systems, e.g., by maps) in a random environment: the animals use their intelligence and experience to guide them. The more knowledge an ant has, the higher its foraging efficiency is. When young insects join the collective to forage with old and middle-aged ants, it benefits the whole colony in the long run. The resulting strategy can even be optimal.