多维混沌映射动力学选择自由度的共振强迫
Resonant forcing of select degrees of freedom of multidimensional chaotic map dynamics
摘要：
研究了多维混沌映射动力学的共振现象。我们使用的变分法，以确定的附加强制功能，诱导最大的响应，也就是说，从未扰动的动态最大的偏差。我们包括额外的约束，只有选择自由度被强迫，对应于一个非常一般的一类问题，其中并不是所有的自由度在一个实验系统是可访问的强迫。我们发现，某些拉格朗日乘子采取了一个基本的物理作用的效率的强制功能和有效的强迫所经历的自由度，而不是直接被迫。此外，我们发现附近轨迹的位移和有效总强迫函数的乘积是一个守恒量。我们用几个例子证明了这种方法的有效性。
英文摘要：
We study resonances of multidimensional chaotic map dynamics. We use the calculus of variations to determine the additive forcing function that induces the largest response, that is, the greatest deviation from the unperturbed dynamics. We include the additional constraint that only select degrees of freedom be forced, corresponding to a very general class of problems in which not all of the degrees of freedom in an experimental system are accessible to forcing. We find that certain Lagrange multipliers take on a fundamental physical role as the efficiency of the forcing function and the effective forcing experienced by the degrees of freedom which are not forced directly. Furthermore, we find that the product of the displacement of nearby trajectories and the effective total forcing function is a conserved quantity. We demonstrate the efficacy of this methodology with several examples.
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