STUDY OF NOISE-INDUCED TRANSITIONS IN THE LORENZ SYSTEM USING THE MINIMUM ACTION METHOD
STUDY OF NOISE-INDUCED TRANSITIONS IN THE LORENZ SYSTEM USING THE MINIMUM ACTION METHOD
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DOI：
10.4310/cms.2010.v8.n2.a3
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发表时间：
2010-06
影响因子：
1
通讯作者：
Xiang Zhou;Andrew Majda
中科院分区：
文献类型：
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作者：
Xiang Zhou;Andrew Majda
我们研究了当复数不变集出现时，非梯度系统中的噪声诱导跃迁。我们的例子是三个具有代表性的瑞利数区域中的洛伦兹系统。研究发现，在同宿爆炸分叉之前，唯一的过渡态是鞍点，且过渡态类似于梯度系统的过渡态。然而，当混沌不变集出现时，一个不稳定的极限环从同宿轨迹继续。这个轨道嵌入在围绕初始稳定驻点的局部管状流形中，作为相对吸引子，在跃迁过程中扮演着最可能的出口集的角色。这个例子展示了极限环是如何在光滑动力系统的过渡过程中涉及到的，极限环是超越不动点的下一个最简单的不变集。
We investigate noise-induced transitions in non-gradient systems when complex invariant sets emerge. Our example is the Lorenz system in three representative Rayleigh number regimes. It is found that before the homoclinic explosion bifurcation, the only transition state is the saddle point, and the transition is similar to that in gradient systems. However, when the chaotic invariant set emerges, an unstable limit cycle continues from the homoclinic trajectory. This orbit, which is embedded in a local tube-like manifold around the initial stable stationary point as a relative attractor, plays the role of the most probable exit set in the transition process. This example demonstrates how limit cycles, the next simplest invariant set beyond fixed points, can be involved in the transition process in smooth dynamical systems.