论文标题
基于盆地熵的分形边界的测试
A test for fractal boundaries based on the basin entropy
论文作者
论文摘要
在动态系统中，吸引力的盆地将相位空间中的一组给定初始条件连接到其渐近状态。盆地熵和相关工具在初始状态中有初始扰动或不确定性时，量化了系统最终状态中的不可预测性。基于盆地熵，$ \ ln 2 $标准允许以固定分辨率对分形盆地边界进行有效测试。在这里，我们将此标准扩展到一个新的测试中，并提高了灵敏度，我们称之为\ textIt {$ s_ {bb} $ fractality test}。使用相同的单个比例信息，$ s_ {bb} $分形测试可以比$ \ ln 2 $标准在许多情况下检测分形边界。用范式驱动的振荡器说明了新的测试，并将结果与不确定性指数给出的经典方法进行了比较。我们认为，这项工作对于研究高维系统和吸引力的实验盆地可能特别有用。
In dynamical systems, basins of attraction connect a given set of initial conditions in phase space to their asymptotic states. The basin entropy and related tools quantify the unpredictability in the final state of a system when there is an initial perturbation or uncertainty in the initial state. Based on the basin entropy, the $\ln 2$ criterion allows for efficient testing of fractal basin boundaries at a fixed resolution. Here, we extend this criterion into a new test with improved sensitivity that we call the \textit{$S_{bb}$ fractality test}. Using the same single scale information, the $S_{bb}$ fractality test allows for the detection of fractal boundaries in many more cases than the $\ln 2$ criterion. The new test is illustrated with the paradigmatic driven Duffing oscillator, and the results are compared with the classical approach given by the uncertainty exponent. We believe that this work can prove particularly useful to study both high-dimensional systems and experimental basins of attraction.
