Chaos–order transition in foraging behavior of ants

Abstract

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 lowdimensional 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.foraging dynamics | learning process | low-dimensional chaos | mathematical modeling | synchronization B oth experimental data analysis and mathematical modeling on the foraging behavior of group animals (especially ant colonies) have recently captured much attention due to the high level of self-organizing structures that emerge at the collective level (1-5). Random walking is a widely discussed strategy in the research literature on the foraging behavior of group animals (2, 6-8). Some ecologists maintain that especially Lévy flight schemes can appropriately be used to describe the foraging behavior (6, 7). However, some recent studies have raised doubts whether this is a valid conjecture (2,8,9). It is even argued that the rules of locomotion for a walker are always consistent with a purely deterministic model, rather than with a stochastic scheme (9, 10).On the other hand, in the studies on the foraging behavior of animals, the existence of homes has so far received relatively little attention. Here we argue that the existence of a home or nest influences the foraging process to a large extent. Animals are due to return to their homes because of increasing exhaustion of energy. Moreover each foraging process of an animal is also a learning process. With foraging repetition, long-term memory continues to accumulate, an animal's knowledge about the environment of its nest gets richer, and the region that the animal is familiar with continues to enlarge. Moreover, animals' physical ability and knowledge as determined by the...

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