We propose a stochastic sampling approach to identify stability boundaries in general dynamical systems. The global landscape of Lyapunov exponent in multi-dimensional parameter space provides transition boundaries for stable/unstable trajectories, i.e., the edge of chaos. Despite its usefulness, it is generally difficult to derive analytically. In this study, we reveal the transition boundaries by leveraging the Markov chain Monte Carlo algorithm coupled directly with the numerical integration of nonlinear differential/difference equation. It is demonstrated that a posteriori modeling for parameter subspace along the edge of chaos determines an inherent constrained dynamical system to flexibly activate or de-activate the chaotic tra jectories.

翻译：本文提出了一种随机采样方法，用于识别一般动力系统中的稳定性边界。多维参数空间中李雅普诺夫指数的全局景观为稳定/不稳定轨迹（即混沌边缘）提供了转变边界。尽管该方法具有实用性，但其解析推导通常较为困难。在本研究中，我们通过将马尔可夫链蒙特卡洛算法与非线性微分/差分方程的数值积分直接耦合，揭示了这些转变边界。研究表明，沿混沌边缘对参数子空间进行后验建模，可确定一个固有的约束动力系统，从而灵活地激活或抑制混沌轨迹。