Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan.
Chaos. 2009 Sep;19(3):033125. doi: 10.1063/1.3211190.
In this paper, we propose a novel model, a delayed transiently chaotic neural network (DTCNN), and numerically confirm that the model performs better in finding the global minimum for the traveling salesman problem (TSP) than the traditional transiently chaotic neural network. The asymptotic stability and chaotic behavior of the dynamical system with time delay are fully discussed. We not only theoretically prove the existence of Marotto's chaos for the delayed neural network without the cooling schedule by geometrically constructing a transversal homoclinic orbit, but we also discuss the stability of nonautonomous delayed systems using LaSalle's invariance principle. The result of the application to the TSP by the DTCNN might further explain the importance of systems with time delays in the neural system.
在本文中，我们提出了一种新的模型，即延迟暂态混沌神经网络（DTCNN），并通过数值验证了该模型在求解旅行商问题（TSP）的全局最小值方面优于传统的暂态混沌神经网络。我们充分讨论了时滞动力系统的渐近稳定性和混沌行为。我们不仅通过几何构造横截同宿轨道，从理论上证明了无冷却方案的时滞神经网络存在 Marotto 混沌，而且还利用 LaSalle 不变原理讨论了非自治时滞系统的稳定性。DTCNN 在 TSP 中的应用结果可能进一步解释了时滞系统在神经网络中的重要性。
