Kozma Robert
Department of Mathematical Sciences, 373 Dunn Hall, University of Memphis, Memphis, TN 38152, USA.
Chaos. 2003 Sep;13(3):1078-89. doi: 10.1063/1.1599991.
This work aims at studying dynamical models of neural networks, which exhibit phase transitions between states of various complexities. We use the biologically motivated KIII model, which has demonstrated excellent performance as a robust dynamical memory device. KIII is a high-dimensional dynamical system with extremely fragmented boundaries between limit cycles, tori, fixed points, and chaotic attractors. We study the role of additive noise in the development of itinerant trajectories. Noise not only stabilizes aperiodic trajectories, but there is an optimum noise level with highly itinerant behavior. We speculate that the previously found optimum classification performance of KIII as a function of the noise level, also identified as chaotic resonance, is related to chaotic itinerant oscillations among various ordered states.
这项工作旨在研究神经网络的动力学模型，该模型展现出不同复杂程度状态之间的相变。我们使用具有生物学动机的KIII模型，它作为一种强大的动态记忆装置已展现出卓越性能。KIII是一个高维动力系统，在极限环、环面、不动点和混沌吸引子之间具有极其破碎的边界。我们研究加性噪声在无规运动轨迹发展中的作用。噪声不仅能稳定非周期轨迹，而且存在一个具有高度无规运动行为的最佳噪声水平。我们推测，之前发现的KIII作为噪声水平函数的最佳分类性能（也被认定为混沌共振）与各种有序状态之间的混沌无规振荡有关。
