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 …

We study a scalar delay differential equation (DDE) with two delayed feedback terms that
depend linearly on the state. The associated constant-delay DDE, obtained by freezing the …

A neural field models the large scale behaviour of large groups of neurons. We extend
previous results for these models by including a diffusion term into the neural field, which …

In this paper, we perform the parameter-dependent center manifold reduction near the
generalized Hopf (Bautin), fold-Hopf, Hopf-Hopf, and transcritical-Hopf bifurcations in delay …

For nonlinear time-delay systems, domains of attraction are rarely studied despite their
importance for technological applications. The present paper provides methodological hints …

A common task when analysing dynamical systems is the determination of normal forms
near local bifurcations of equilibria. As most of these normal forms have been classified and …

Delay Differential Equations (DDEs) appear in many applications, including neuroscience,
ecology, and engineering. The analysis of one-and two-parameter families of bifurcations is …

Recent work in arXiv: 1901.11526 by the author about a class of abstract delay differential
equations (DDEs), as well as earlier work by Diekmann and Gyllenberg on other classes of …

In this paper, we will perform the parameter-dependent center manifold reduction near the
generic and transcritical codimension two Bogdanov–Takens bifurcation in classical delay …

In this paper, we prove the existence of a periodic smooth finite-dimensional center manifold
near a nonhyperbolic cycle in classical delay differential equations by using the Lyapunov …