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不变流形演进方向对非双曲型非线性时间序列重影算法的影响分析The Effects of Homoclinic Tangencies and Homoclinic Intersectionons on Shadowing Algorithm for Series of Non-Hyperbolic Nonlinear Systems
张政伟, 张铭, 樊养余
非双曲型非线性系统, 轨迹重影, Newton-Raphson算法, 梯度下降, 同宿切面, 同宿横截点Non-Hyperbolic Nonlinear System, Shadowing, Newton-Raphson Algorithm, Gradient Descent, Homoclinic Tangencies, Homoclinic Intersections
《Artificial Intelligence and Robotics Research》, Vol.5 No.3, 2016-08-11
The presence of homoclinic tangencies and homoclinic intersections makes it very difficult, sometimes even impossible, to shadow the trajectory of the non-hyperbolic nonlinear system. Different from former methods, this paper analyzed the effects of the homoclinic tangencies on the algorithm, and proposed methods that can decrease, or even avoid the effects. Different from those methods which take it for granted that the failure of denoising algorithms is related with the homoclinic tangencies only, experiments in this paper demonstrate a quantitative correlation between the minimal distance of homoclinic intersections and the standard variance of noise. Thus the probability that the algorithm converges to the true trajectory could be boosted efficiently, and without any doubts, this strategy would be a heuristic approach to other similar methods.