Abstract:
Common tasks in data-driven modeling of nonlinear chaotic systems include estimating unknown model parameters and variables that are unobservable or difficult to measure, as well as implementing feedforward or feedback control schemes to steer the system’s dynamics in a desired direction. We compare and evaluate various methods for addressing these tasks and their application to hyperchaotic spatiotemporal systems, such as the Lorenz-96 model or the Kuramoto-Sivashinsky equation. Particular attention is paid to the dynamics of the myocardium which constitutes an excitable medium. There, the electrical excitation waves that trigger the contraction of the heart muscle can become unstable and transform into chaotic spiral waves, leading to life-threatening arrhythmias that must be immediately terminated using effective control methods. This type of complex cardiac dynamics is often governed by transient chaos, where the temporal evolution exhibits signs of chaos over a (very) long period but eventually becomes periodic or converges to a steady state where the electrical excitation waves disappear. Current research therefore focuses on analyzing the onset, perpetuation and termination of chaos in excitable media where advanced dynamical control strategies could pave the way for novel, efficient, and less invasive defibrillation methods.