论文标题
混沌马鞍中的磁透感模型中的混沌马鞍
Chaotic saddles in a generalized Lorenz model of magnetoconvection
论文作者
论文摘要
研究了最近衍生的广义Lorenz模型（Macek and Strumik，Phys。E82，027301，2010）的非线性动力学。分叉图的构建是瑞利号的函数，其中吸引子和非吸引人的混乱集在周期性窗口内共存。无吸引的混乱集（也称为混乱的马鞍）是造成分形盆地边界的，其分形维度附近相位空间的尺寸，这会导致很长的混乱瞬变。结果表明，混乱的马鞍可用于推断周期窗口外混沌吸引子的特性，例如其最大Lyapunov指数。
The nonlinear dynamics of a recently derived generalized Lorenz model (Macek and Strumik, Phys. Rev. E 82, 027301, 2010) of magnetoconvection is studied. A bifurcation diagram is constructed as a function of the Rayleigh number where attractors and nonattracting chaotic sets coexist inside a periodic window. The nonattracting chaotic sets, also called chaotic saddles, are responsible for fractal basin boundaries with a fractal dimension near the dimension of the phase space, which causes the presence of very long chaotic transients. It is shown that the chaotic saddles can be used to infer properties of chaotic attractors outside the periodic window, such as their maximum Lyapunov exponent.
