title: 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 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.
authors.affiliation: Information Security Center, State Key Laboratory of Networking and Switching Technology, andPotsdam Institute for Climate Impact Research, D14473 Potsdam, Germany; and.
authors.forename: Lixiang
authors.initials: L
authors.lastname: Li
authors.affiliation: Information Security Center, State Key Laboratory of Networking and Switching Technology, and kurths@pik-potsdam.de penghaipeng@bupt.edu.cn director@pik-potsdam.de.
authors.forename: Haipeng
authors.initials: H
authors.lastname: Peng
authors.affiliation: Potsdam Institute for Climate Impact Research, D14473 Potsdam, Germany; and kurths@pik-potsdam.de penghaipeng@bupt.edu.cn director@pik-potsdam.de.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Kurths
authors.affiliation: Information Security Center, State Key Laboratory of Networking and Switching Technology, andNational Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing 100876, China;
authors.forename: Yixian
authors.initials: Y
authors.lastname: Yang
authors.affiliation: Potsdam Institute for Climate Impact Research, D14473 Potsdam, Germany; andSanta Fe Institute, Santa Fe, NM 87501 kurths@pik-potsdam.de penghaipeng@bupt.edu.cn director@pik-potsdam.de.
authors.forename: Hans Joachim
authors.initials: HJ
authors.lastname: Schellnhuber
mesh_terms: D000367:Age Factors; D000465:Algorithms; D000818:Animals; D001000:Ants / Q000502:physiology*; D001070:Appetitive Behavior / Q000502:physiology*; D003198:Computer Simulation; D005106:Exploratory Behavior / Q000502:physiology; D005247:Feeding Behavior / Q000502:physiology*; D006702:Homing Behavior / Q000502:physiology; D008954:Models, Biological; D011340:Problem Solving / Q000502:physiology; D012919:Social Behavior
keywords: foraging dynamics; learning process; low-dimensional chaos; mathematical modeling; synchronization