balancing robustness against the dangers of multiple attractors in a hopfield-type model of biological attractors平衡鲁棒性攻击的危险多个hopfield-type模型生物吸引子的吸引子.pdf

Balancing Robustness against the Dangers of Multiple Attractors in a Hopfield-Type Model of Biological Attractors 1 2 Ron C. Anafi , Jason H. T. Bates * 1 Division of Sleep Medicine, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America, 2 Department of Medicine, University of Vermont, Burlington, Vermont, United States of America Abstract Background: Many chronic human diseases are of unclear origin, and persist long beyond any known insult or instigating factor. These diseases may represent a structurally normal biologic network that has become trapped within the basin of an abnormal attractor. Methodology/Principal Findings: We used the Hopfield net as the archetypical example of a dynamic biological network. By progressively removing the links of fully connected Hopfield nets, we found that a designated attractor of the nets could still be supported until only slightly more than 1 link per node remained. As the number of links approached this minimum value, the rate of convergence to this attractor from an arbitrary starting state increased dramatically. Furthermore, with more than about twice the minimum of links, the net became increasingly able to support a second attractor. Conclusions/Significance: We speculate that homeostatic biological networks may have evolved to assume a degree of connectivity that balances robustness and agility against the dangers of becoming trapped in an abnormal attractor. Citation: Anafi RC, Bates JHT (2010) Balancing Robustness against the Dangers of Multiple Attractors in a Hopfield-Type Model of Biological Attractors. PLoS ONE 5(12): e14413. doi:10.1371/journal.pone.0014413 Editor: Jean Peccoud, Virginia Tech, United States of America Received April 27, 2010; Accepted December 6, 2010; Published December 22, 2010 Copyright: 2010 Anafi,