Numerical methods for stochastic sensitivity analysis of 2D chaotic attractors

Abstract

The paper presents constructive algorithms for finding the outer boundaries of chaotic attractors, based on a geometric selection of points of critical lines belonging only to the outer boundary. In the theory of dynamical discrete-time systems, critical lines play a key role. These lines facilitate the study of the dynamic properties of noninvertible maps and to describe the boundaries of a chaotic attractor. The previously constructed stochastic sensitivity function for chaotic attractors is based on critical lines and lets us estimate the dispersion of random states around the chaotic attractor. However, the technical problem is complicated by the fact that the critical lines describe not only the external boundaries, but also structures inside the chaotic attractor. Our algorithms are tested for complex non-convex forms of chaotic attractors. Based on the algorithms, we solve the problem of finding confidence domains around chaotic attractors of stochastic systems. © 2022 Author(s).