title: Dynamical singularities in adaptive delayed-feedback control.
abstract: We demonstrate the dynamical characteristics of adaptive delayed-feedback control systems, exploiting a discrete-time adaptive control method derived for carrying out detailed analysis. In particular, the systems exhibit singularities such as power-law decay of the distribution of transient times and almost zero finite-time Lyapunov exponents. We can explain these results by characterizing such systems as having (1) a Jacobian matrix with unity eigenvalue in the whole phase space, and (2) parameters approaching a stability boundary proven to be identical with that of (nonadaptive) delayed-feedback control.
authors: Future University Hakodate, 116-2 Kameda Nakano-cho, Hakodate, Hokkaido 041-8655, Japan. saito@fun.ac.jp
authors: Asaki
authors: A
authors: Saito
authors: Keiji
authors: K
authors: Konishi
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D005246:Feedback; D008962:Models, Theoretical