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Chaotic Saddles in a Generalized Lorenz Model of Magnetoconvection
International Journal of Bifurcation and Chaos ( IF 2.2 ) Pub Date : 2020-10-05 , DOI: 10.1142/s0218127420300347
Francis F. Franco 1 , Erico L. Rempel 2
Affiliation  

The nonlinear dynamics of a recently derived generalized Lorenz model [ Macek & Strumik, 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.

中文翻译:

磁对流广义洛伦兹模型中的混沌鞍座

研究了最近导出的磁对流广义 Lorenz 模型 [ Macek & Strumik, 2010 ] 的非线性动力学。分岔图是作为瑞利数的函数构造的,其中吸引子和非吸引混沌集在周期窗口内共存。非吸引混沌集,也称为混沌鞍,是分形盆地边界的原因,其分形维数接近相空间的维数,导致存在很长的混沌瞬变。结果表明,混沌鞍可用于推断周期窗外混沌吸引子的性质,例如它们的最大 Lyapunov 指数。
更新日期:2020-10-05
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