The discrete Lyapunov function for scalar differential delay equations

Lyapunov-Krasovskii functionals for scalar neutral type time delay equations

In this paper a procedure for construction of complete type Lyapunov–Krasovskii functionals for a scalar neutral type time delay equation is considered. The construction of the functionals depends on the so-called Lyapunov functions which satisfy a delay equation with additional boundary conditions. It is shown that these functionals admit lower and upper quadratic bounds. Exponential estimates...

Moment Lyapunov Exponent of Delay Differential Equations

The aim of this paper is to establish a connecting thread through the probabilistic concepts of pth-moment Lyapunov exponents, the integral averaging method, and Hale’s reduction approach for delay dynamical systems. We demonstrate this connection by studying the stability of perturbed deterministic and stochastic differential equations with fixed time delays in the displacement and derivative ...

Global stability of the equilibrium for scalar delay differential equations

This version has a lot of inserted Comments to indicate what must be done and what will be in here when this is completed. [These Comments also note open questions, where possible, so for suggested results not noted as open one may assume the proofs are known, even if not yet included.] This was originally intended as a revised version of what became [5] before publication, then became comments...

Spectrum and amplitude equations for scalar delay-differential equations with large delay

The subject of the paper are scalar delay-differential equations with large delay. Firstly, we describe the asymptotic properties of the spectrum of linear equations. Using these properties, we classify possible types of destabilization of steady states. In the limit of large delay, this classification is similar to the one for parabolic partial differential equations. We present a derivation a...

Discrete Collocation Method for Solving Fredholm Volterra Intergro-Differential Equations