Global organization of phase space in the transition to chaos in the Lorenz system
Global organization of phase space in the transition to chaos in the Lorenz system
复制标题
洛伦兹系统向混沌过渡过程中相空间的全局组织
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
H. Osinga
中科院分区：
文献类型：
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作者：
E. Doedel;B. Krauskopf;H. Osinga
在洛伦兹系统的混沌过渡-从简单的通过preturbulent混沌动力学-已被表征的动力学和各自的吸引子，如所描述的一维洛伦兹映射。在本文中，我们考虑这种转变如何体现自己的全球性，也就是说，我们确定了整个相空间的相关组织。为此，我们研究如何全局不变流形的平衡和周期轨道的参数变化，在这种情况下的主要研究对象是二维（2D）稳定流形的起源，或洛伦兹流形。我们利用边值问题的方法计算二维整体流形及其与球面的复杂交集。这使我们能够确定如何吸引盆地的变化或创建，并给出一个精确的表征所观察到的拓扑和几何性质的相关二维不变流形在过渡期间。
The transition to chaos in the Lorenz system—from simple via preturbulent to chaotic dynamics—has been characterized in terms of the dynamics and the respective attractors, as described by the one-dimensional Lorenz map. In this paper we consider how this transition manifests itself globally, that is, we determine the associated organization of the entire phase space. To this end, we study how global invariant manifolds of equilibria and periodic orbits change with the parameters; the main object of study in this context is the two-dimensional (2D) stable manifold of the origin, or Lorenz manifold. We compute two-dimensional global manifolds and their complicated intersection sets with a sphere by using a boundary value problem setup. This allows us to determine how basins of attraction change or are created, and to give a precise characterization of the observed topological and geometric properties of the relevant 2D invariant manifolds during the transition.