29.06.2026 15:00 Lion Reichl:
Stability and Robustness of the Echo State Property (ESP) in Continuous TimeMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)
Echo state networks (ESNs) are recurrent models whose stability and memory properties are often summarized by the echo state property (ESP). This thesis develops a continuous-time ESN framework in the language of non-autonomous dynamical systems using the skew-product formalism. Building on this setting, we introduce an input-wise notion of multistability through an echo index, which measures the number of attracting solutions induced by a fixed input signal. We provide sufficient conditions guaranteeing echo index one, including contraction- type regimes and large-input regimes, and study robustness under perturbations of the input signal.