Abstract Dynamics: An Alternative Approach to Local Lyapunov Exponents in Examining Local Unpredictability

This chapter proposes a computational approach that has its roots in the early ideas of local Lyapunov exponents, yet it offers new perspectives toward analyzing these problems. The method of interest, namely abstract dynamics, is an indirect quantitative measure of the variations of the governing vector fields based on the principles of linear systems. The examples in this work, ranging from simple limit cycles to chaotic attractors, are indicative of the new interpretation that this new perspective can offer. The presented results can be exploited in the structure of algorithms (most prominently machine learning algorithms) that are designed to estimate the complex behavior of nonlinear systems, even chaotic attractors, within their horizon of predictability.