Universal dichotomy for dynamical systems with variable delay
We show that the dynamics of systems with a time-dependent delay is fundamentally
affected by the functional form of the retarded argument. Associating with the latter an
iterated map, the access map, and a corresponding Koopman operator, we identify two
universality classes. Members in the first are equivalent to systems with a constant delay.
The new, second class is characterized by the mode-locking behavior of their access maps
and by an asymptotically linear, instead of a logarithmic, scaling of the Lyapunov spectrum …
affected by the functional form of the retarded argument. Associating with the latter an
iterated map, the access map, and a corresponding Koopman operator, we identify two
universality classes. Members in the first are equivalent to systems with a constant delay.
The new, second class is characterized by the mode-locking behavior of their access maps
and by an asymptotically linear, instead of a logarithmic, scaling of the Lyapunov spectrum …
A universal dichotomy for dynamical systems with variable delay
We show that the dynamics of systems with time-dependent delay is fundamentally affected
by the functional form of the retarded argument. Associating to the latter an iterated map, the
access map, and a corresponding Koopman operator, we identify two universality classes.
Members in the first are equivalent to systems with constant delay. The new, second class is
characterized by modelocking behavior of their access maps and by an asymptotically
linear, instead of a logarithmic scaling of the Lyapunov spectrum. The membership depends …
by the functional form of the retarded argument. Associating to the latter an iterated map, the
access map, and a corresponding Koopman operator, we identify two universality classes.
Members in the first are equivalent to systems with constant delay. The new, second class is
characterized by modelocking behavior of their access maps and by an asymptotically
linear, instead of a logarithmic scaling of the Lyapunov spectrum. The membership depends …