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arXiv 2402.03514nlin.CD
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盆地熵作为时滞系统分岔的指标

Basin entropy as an indicator of a bifurcation in a time-delayed system

Juan Pedro Tarigo, Cecilia Stari, Cristina Masoller, Arturo C. Marti

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6 pages, 7 figs
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AI总结：

本研究提出将盆地熵应用于时滞双稳态系统，发现其能反映吸引盆特性并指示Hopf分岔接近度，但无法指示叉形分岔，为时滞系统长期可预测性提供新视角。

摘要：

盆地熵是一种度量，用于量化具有两个或更多吸引子的系统中，最终状态作为初始条件函数的可预测性。尽管盆地熵已在多种多稳态动力系统上得到验证，但据我们所知，它尚未在具有时滞的系统中进行测试，此类系统的相空间是无限维的，因为初始条件是定义在时间区间$[-τ,0]$上的函数，其中$τ$为延迟时间。在此，我们考虑一个简单的时滞系统，该系统由一个具有线性延迟反馈项的双稳态系统组成。我们表明，盆地熵能够捕捉两个共存吸引子的吸引盆的相关性质。此外，我们表明，盆地熵可以指示Hopf分岔的接近程度，但无法捕捉叉形分岔的接近程度。我们的结果表明，盆地熵可以为时滞系统的长期可预测性提供有用的见解，此类系统通常具有共存的吸引子。

英文摘要：

The basin entropy is a measure that quantifies, in a system that has two or more attractors, the predictability of a final state, as a function of the initial conditions. While the basin entropy has been demonstrated on a variety of multistable dynamical systems, to the best of our knowledge, it has not yet been tested in systems with a time delay, whose phase space is infinite dimensional because the initial conditions are functions defined in a time interval $[-τ,0]$, where $τ$ is the delay time. Here we consider a simple time delayed system consisting of a bistable system with a linear delayed feedback term. We show that the basin entropy captures relevant properties of the basins of attraction of the two coexisting attractors. Moreover, we show that the basin entropy can give an indication of the proximity of a Hopf bifurcation, but fails to capture the proximity of a pitchfork bifurcation. Our results suggest that the basin entropy can yield useful insights into the long-term predictability of time delayed systems, which often have coexisting attractors.

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