Analysis of chaotic dynamical systems with autoencoders

Nonlinear dynamical systems, either continuous or discrete, may produce chaos, i.e. irregular evolution similar to probabilistic, stochastic motion. Continuous autonomous chaotic systems are described by at least three coupled ordinary nonlinear differential equations that, when solved numerically, result in trajectories with irregular features. In general, non-Hamiltonian cases, the trajectory may fall on a strange attractor that is a chaotic yet distinct structure in the system phase space. Understanding the complex dynamics in phase space is significant especially in the mathematical analysis of the inverse problem. In the latter we are given a time series of discrete data and we want to find whether this set derives from a chaotic dynamical system or it is purely stochastic [1-4].