Data-Driven Detection and Classification of Regimes in Chaotic Systems Via Hidden Markov Modeling

Chaotic dynamical systems are essentially nonlinear and are highly sensitive to variations in initial conditions and process parameters. Chaos may appear both in natural (e.g., heartbeat rhythms and weather fluctuations) and human-engineered (e.g., thermo-fluid, urban traffic, and stock market) systems. For prediction and control of such systems, it is often necessary to be able to distinguish between non-chaotic and chaotic behavior; several methods exist to detect the presence (or absence) of chaos, specially in noisy signals. A dynamical system may exhibit multiple chaotic regimes, and apparently, there exist no methods, reported in open literature, to classify these regimes individually. This paper demonstrates an application of standard hidden Markov modeling (HMM), which is a commonly used supervised method, as a technique to classify multiple regimes from a time series of dynamical systems, where classified regimes could be chaotic or non-chaotic. The proposed HMM-based method of regime classification has been tested using numerical data obtained from several well-known chaotic dynamical systems (e.g., Hénon, forced Duffing, Rössler, and Lorenz attractor). It is apparently well-suited to serve as a bench mark for the development of alternative data-driven methods to enhance the performance (e.g., accuracy and computational speed) of regime classification in chaotic dynamical systems.