论文标题
耗散孤子的混沌扩散：从反抗性随机步行到隐藏的马尔可夫模型
Chaotic Diffusion of Dissipative Solitons: From Anti-Persistent Random Walk to Hidden Markov Models
论文作者
论文摘要
在先前的出版物中，我们表明，在典型的复杂复杂的Ginzburg-landau方程中，耗散孤子的混乱扩散的增量过程，例如，从非线性光学器件中已知，由简单的马尔可夫过程控制，导致一个带有更复杂的动作或更复杂的隐藏Markov Markov模型，具有持续的持续性输出输出型。在本文中，我们通过研究孤子动力学来揭示这两个模型之间的过渡，以依赖于金兹堡 - 陆克方程的主要分叉参数并确定基本的隐藏马尔可夫过程。这些模型捕获了代表孤子运动的跳跃宽度和符号序列中相关性的非平凡衰减，反持有步行情节的统计数据以及跳跃宽度的多模式密度。我们证明，在物理上有意义地减少了无限维确定性系统的动力学，以概率有限状态机器之一，并在基础非线性动力学的参数变化下更深入地了解孤子动力学。
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.
