Asymptotic methods for delay equations

Asymptotic methods for delay equations

Asymptotic methods for singularly perturbed delay differential equations are in many ways more challenging to implement than for ordinary differential equations. In this paper, four examples of delayed systems which occur in practical models are considered: the delayed recruitment equation, relaxation oscillations in stem cell control, the delayed logistic equation, and density wave oscillation...

Asymptotic Methods for Differential Equations

adrian muntean university of eindhoven [email protected] antonios zagaris university of twente [email protected]

Global asymptotic behavior for delay dynamic equations

We give conditions under which the trivial solution of a first-order nonlinear variable-delay dynamic equation is asymptotically stable, for arbitrary time scales that are unbounded above. In an example, we apply our techniques to a logistic dynamic equation on isolated, unbounded time scales. c © 2006 Elsevier Ltd. All rights reserved. MSC: 39A10; 34B10

Some Asymptotic Methods for Strongly Nonlinear Equations

Asymptotic Behaviours of Stochastic Differential Delay Equations

Most of the existing results on stochastic stability use a single Lyapunov function, but we shall instead use multiple Lyapunov functions in this paper. We shall establish the sufficient condition, in terms of multiple Lyapunov functions, for the asymptotic behaviours of solutions of stochastic differential delay equations. Moreover, from them follow many effective criteria on stochastic asympt...