标题： 非线性动力系统混沌边缘的景观计算 显示英文标题

标题： Landscape computations for the edge of chaos in nonlinear dynamical systems

摘要： 我们提出了一种随机抽样的方法来识别一般动力系统的稳定性边界。多维参数空间中Lyapunov指数的全局景观提供了稳定/不稳定轨迹的过渡边界，即混沌边缘。尽管它很有用，但通常难以解析推导。在这项研究中，我们通过结合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，揭示了这些过渡边界。结果表明，在混沌边缘对参数子空间的后验建模确定了一个内在受限的动力系统，可以灵活地激活或停用混沌轨迹。 显示英文摘要

摘要： 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.