Landscape computations for the edge of chaos in nonlinear dynamical systems

Abstract

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.