KNEADINGS, SYMBOLIC DYNAMICS AND PAINTING LORENZ CHAOS
KNEADINGS, SYMBOLIC DYNAMICS AND PAINTING LORENZ CHAOS
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DOI：
10.1142/s0218127412300169
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发表时间：
2012-04-01
影响因子：
2.2
通讯作者：
Shilnikov, Leonid
中科院分区：
文献类型：
--
作者：
Barrio, Roberto;Shilnikov, Andrey;Shilnikov, Leonid
提出了一种新的利用捏合不变量进行符号描述的计算方法，并对几个具有Lorenz吸引子的典型系统的动力学和参数混沌的研究进行了验证。该技术可以揭示双参数结构令人震惊的复杂性和普遍性，并在基于捏合的扫描中检测它们的组织中心-余维-来自流体力学的标志性洛伦兹方程的两个T点和分离的鞍座，来自数学的普通模型，以及来自非线性光学的激光模型。
A new computational technique based on the symbolic description utilizing kneading invariants is proposed, and verified for explorations of dynamical and parametric chaos in a few exemplary systems with the Lorenz attractor. The technique allows for uncovering the stunning complexity and universality of bi-parametric structures and detects their organizing centers - codimension-two T-points and separating saddles in the kneading-based scans of the iconic Lorenz equation from hydrodynamics, a normal model from mathematics, and a laser model from nonlinear optics.