arXiv 2201.124712022-01-29nlin.CD

耗散孤子的混沌扩散：从反持续随机游动到隐马尔可夫模型

Chaotic Diffusion of Dissipative Solitons: From Anti-Persistent Random Walk to Hidden Markov Models

Tony Albers, Jaime Cisternas, Günter Radons

备注：: 16 pages, 12 figures, 2 tables
DOI：: 10.1016/j.chaos.2022.112290

摘要：

在以前的文献中，我们证明了在一个典型的复Ginzburg-Landau方程中耗散孤子的混沌扩散的增量过程，例如，从非线性光学，是由一个简单的马尔可夫过程，导致一个反持久性随机游走的运动或由一个更复杂的隐马尔可夫模型与连续输出密度。在这篇文章中，我们揭示了这两个模型之间的过渡，通过研究孤子动力学的主要分歧参数的金斯堡-朗道方程和识别潜在的隐马尔可夫过程的依赖。这些模型捕获的跳跃宽度和符号序列的相关性的非平凡衰减表示的孤子运动，反持续行走情节的统计，和多峰密度的跳跃宽度。我们证明，存在一个物理意义的减少一个无限维的确定性系统的动力学的概率有限状态机之一，并提供了一个更深入的了解孤子动力学参数变化的基础非线性动力学。

英文摘要：

In previous publications, we showed that the incremental process of the chaotic diffusion of dissipative solitons in a prototypical complex Ginzburg-Landau equation, known, e.g., from nonlinear optics, is governed by a simple Markov process leading to an Anti-Persistent Random Walk of motion or by a more complex Hidden Markov Model with continuous output densities. In this article, we reveal the transition between these two models by studying the soliton dynamics in dependence on the main bifurcation parameter of the Ginzburg-Landau equation and identify the underlying hidden Markov processes. These models capture the non-trivial decay of correlations in jump widths and symbol sequences representing the soliton motion, the statistics of anti-persistent walk episodes, and the multimodal density of the jump widths. We demonstrate that there exists a physically meaningful reduction of the dynamics of an infinite-dimensional deterministic system to one of a probabilistic finite state machine and provide a deeper understanding of the soliton dynamics under parameter variation of the underlying nonlinear dynamics.

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摘要：

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