Predicting the bounds of large chaotic systems using low-dimensional manifolds.

ABSTRACT: Predicting extrema of chaotic systems in high-dimensional phase space remains a challenge. Methods, which give extrema that are valid in the long term, have thus far been restricted to models of only a few variables. Here, a method is presented which treats extrema of chaotic systems as belonging to discretised manifolds of low dimension (low-D) embedded in high-dimensional (high-D) phase space. As a central feature, the method exploits that strange attractor dimension is generally much smaller than parent system phase space dimension. This is important, since the computational cost associated with discretised manifolds depends exponentially on their dimension. Thus, systems that would otherwise be associated with tremendous computational challenges, can be tackled on a laptop. As a test,

SUBMITTER: Haugaard AM 

PROVIDER: S-EPMC5482462 | biostudies-literature | 2017

REPOSITORIES: biostudies-literature