Regime-Switching Dynamical Systems

Regime-switching dynamical systems describe processes whose behavior changes between modes, such as stable and event-driven market periods, neural states, or operating conditions in a robot. Researchers use Markov-switching and state-space models, piecewise-smooth equations, change-point detection, and neural approaches such as mixtures of experts to infer regimes and their dynamics. These methods support forecasting, causal analysis, anomaly detection, and control, with evaluations spanning synthetic benchmarks, financial time series, neural recordings, and physical systems. A central challenge is balancing flexible models that capture nonlinear transitions with reliable recovery of regime boundaries and within-regime dynamics, especially when some modes are rarely observed or added experts distort temporal structure.