用临界慢化检验低耗散动力系统的分岔
Testing Critical Slowing Down as a Bifurcation Indicator in a Low-dissipation Dynamical System
摘要：
我们研究了一个二维低耗散动力系统的控制参数是线性扫过跨临界分岔的时间。我们调查的松弛时间的扰动施加到系统的变量，我们表明，临界减速可能会发生在一个参数值远高于分叉点。我们通过实验测试临界减速的发生施加扰动的可访问的控制参数，我们发现，这种扰动离开系统的行为不变，从而提供没有有用的信息发生临界减速。理论分析揭示了这些检验在预测即将到来的分岔时失败的原因。
英文摘要：
We study a two-dimensional low-dissipation dynamical system with a control parameter that is swept linearly in time across a transcritical bifurcation. We investigate the relaxation time of a perturbation applied to a variable of the system and we show that critical slowing down may occur at a parameter value well above the bifurcation point. We test experimentally the occurrence of critical slowing down by applying a perturbation to the accessible control parameter and we find that this perturbation leaves the system behavior unaltered, thus providing no useful information on the occurrence of critical slowing down. The theoretical analysis reveals the reasons why these tests fail in predicting an incoming bifurcation.
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