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Swarms, Phase Transitions, and Collective Intelligence (Paper 1); and A Nonequilibrium Statistical Field Theory of Swarms and Other Spatially Extended Complex Systems (Paper 2)

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  • Mark M. Millonas

Abstract

(Paper 1) A spacially extended model of the collective behavior of a large number of locally acting organisms is proposed in which organisms move probabilistically between local cells in space, but with weights dependent on local morphogenetic substances, or morphogens. The morphogens are in turn effected by the passage of an organism. The evolution of the morphogens, and the corresponding flow of the organisms constitutes the collective behavior of the group. Such models have various types of phase transitions and self-organizing properties controlled both by the level of the noise, and other parameters. The model is then applied to the specific case of ants moving on a lattice. The local behavior of the ants is inspired by the actual behavior observed in the laboratory, and analytic results for the collective behavior are compared to the corresponding laboratory results. It is hoped that the present model might serve as a paradigmatic example of a complex cooperative system in nature. In particular swarm models can be used to explore the relation of nonequilibrium phase transitions to at least three important issues encountered in artificial life. Firstly, that of emergence as complex adaptive behavior. Secondly, as an exporation of continuous phase transitions in biological systems. Lastly, to derive behavioral criteria for the evolution of collective behavior in social organisms. (Paper 2) A class of models with applications to swarm behavior as well as many other types of spatially extended complex biological and physical systems is studied. Internal fluctuations can play an active role in the organization of the phase structure of such systems. Consequently, it is not possible to fully understand the behavior of these systems without explicitly incorporating the fluctuations. In particular, for the class of models studied here the effect of internal fluctuations due to finite size is a renormalized {\it decrease} in the temperature near the point of spontaneous symmetry breaking. We briefly outline how these models can be applied to the behavior of an ant swarm.

Suggested Citation

  • Mark M. Millonas, 1993. "Swarms, Phase Transitions, and Collective Intelligence (Paper 1); and A Nonequilibrium Statistical Field Theory of Swarms and Other Spatially Extended Complex Systems (Paper 2)," Working Papers 93-06-039, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:93-06-039
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    1. L. Ingber, 1993. "Adaptive Simulated Annealing (ASA)," Lester Ingber Software asa, Lester Ingber.
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