A model of how the local scent laying and scent following of individual ants leads to collective decision making in groups of ants is studied. We confine ourselves here to ants whose motion is restricted to a set of n paths, or one-dimensional segments, connected in an arbitrary way to other segments forming a network. These networks are analogous to some recent laboratory experiments with ants. A microscopic approach is used, where the behavior of the individual ants is completely described by a local choice function based on their observed local behavior. This function gives the allowed transition probabilities to go from a given segment to a final segment in terms of the scents on these final segments. The ants are shown to be analogous to particles with n energy states in equilibrium with a heat bath of a given temperature. The energies of these states evolve according to a set of non-linear differential equations. The various self-organizing and emergent behaviors of groups of ants can then be viewed as instabilities in the dynamics of these equations. The simplest cases where the ants collectively choose between routes of equal and unequal length, and between food sources of varying quality, are examined in detail, and comparisons made with the experimental results (Pasteels et al., 1987a; Deneubourg et al., 1990; Goss et al., 1990). Such ant networks are connectionist type models whose architecture and dynamics parallel those of many interesting systems such as neural networks, autocatalytic chemical reactions (Farmer et al., 1986b), classifier systems, and immune networks (Farmer, 1990). © 1992 Academic Press Limited.
