Real-world systems can be strongly influenced by time delays occurring in self-coupling
interactions, due to unavoidable finite signal propagation velocities. When the delays …

The time needed to exchange information in the physical world induces a delay term when
the respective system is modeled by differential equations. Time delays are hence …

Time-delayed dynamical systems materialize in situations where distant, pointwise,
nonlinear nodes exchange information that propagates at a finite speed. However, they are …

In this paper we give a profound insight into the computation capability of delay based
reservoir computing via an eigenvalue analysis. We concentrate on the task-independent …

Time delayed dynamical systems have proven to be a fertile framework for the study of
physical phenomena. In natural sciences, their uses have been limited to the study of …

Motionless domain walls representing connecting temporal or spatial orbits typically exist
only for very specific parameters, around the so-called Maxwell point. This report introduces …

The time-delayed Adler equation is the simplest model for an injected semiconductor laser
with coherent injection and optical feedback. It is, however, able to reproduce the existence …

We show that delay-differential equations (DDE) exhibit universal bifurcation scenarios,
which are observed in large classes of DDEs with a single delay. Each such universality …

An equilibrium of a delay differential equation (DDE) is absolutely stable, if it is locally
asymptotically stable for all delays. We present criteria for absolute stability of DDEs with …

Dynamical systems with multiple, hierarchically long-delayed feedback are introduced and
studied extending our previous work [Yanchuk and Giacomelli, Phys. Rev. Lett. 112, 174103 …