Deterministic continuous-time models in the sciences often take the form of an ordinary
differential equation. When the system under scrutiny is assumed to be free of external …

In some cases of delay differential equations (DDEs), a delaydependant coefficient is
incorporated into models which takes the form of a function of delay quantity. This brings …

The key idea of the normal form (nf) technique is to transform a nonlinear differential
equation into an equation with a simpler analytic expression, called a normal form, which …

We present a new version of a local Hopf BifurcationTheorem which is applicable to delay
differential equations withstate dependent delays. The smoothness-hypotheses which are …

A previously derived algorithm for the analysis of the Hopf bifurcation in functional
differential equations is extended, allowing the elementary approximation of an existence …

∫− Page 1 On the Bautin bifurcation for systems of delay differential equations Anca–Veronica
Ion University of Piteşti, Târgu din Vale, nr.1, Piteşti, Romania Abstract. For systems of delay …

Smooth ordinary Delay Differential Equations (DDEs) appear in many applications,
including neuroscience, ecology, and engineering. The theory of local bifurcations in one …

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 …

DDEBIFTOOL is a collection of Matlab routines for numerical bifurcation analysis of systems
of delay differential equations with discrete constant and state-dependent delays. The …

This class of equations is widely used in many research fields—it can be obtained through
the linearization of different nonlinear problems (see, for example, Sect. 8.5)—such as …