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Delay Differential Equation (delay + differential_equation)

Distribution by Scientific Domains

Mathematics and Statistics	100%

Selected Abstracts

Global stability and the Hopf bifurcation for some class of delay differential equation

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 10 2008
Marek Bodnar
Abstract In this paper, we present an analysis for the class of delay differential equations with one discrete delay and the right-hand side depending only on the past. We extend the results from paper by U. Fory, (Appl. Math. Lett. 2004; 17(5):581,584), where the right-hand side is a unimodal function. In the performed analysis, we state more general conditions for global stability of the positive steady state and propose some conditions for the stable Hopf bifurcation occurring when this steady state looses stability. We illustrate the analysis by biological examples coming from the population dynamics. Copyright © 2007 John Wiley & Sons, Ltd. [source]

On a linear differential equation with a proportional delay

MATHEMATISCHE NACHRICHTEN, Issue 5-6 2007
ermák
Abstract This paper deals with the delay differential equation We impose some growth conditions on c, under which we are able to give a precise description of the asymptotic properties of all solutions of this equation. Although we naturally have to distinguish the cases c eventually positive and c eventually negative, we show a certain resemblance between the asymptotic formulae corresponding to both cases. Moreover, using the transformation approach we generalize these results to the equation with a general form of a delay. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Positive solutions of a higher order neutral differential equation

MATHEMATISCHE NACHRICHTEN, Issue 1 2003
John R. Graef
Abstract In this paper, we consider the higher order neutral delay differential equation where p : [0, ,) , (0, ,) is a continuous function, r > 0 and , > 0 are constants, and n > 0 is an odd integer. A positive solution x(t) of Eq. (*) is called a Class,I solution if y(t) > 0 and y,(t) < 0 eventually, where y(t) = x(t) , x(t , r). We divide Class,I solutions of Eq. (*) into four types. We first show that every positive solution of Eq. (*) must be of one of these four types. For three of these types, a necessary and sufficient condition is obtained for the existence of such solutions. A necessary condition for the existence of a solution of the fourth type is also obtained. The results are illustrated with examples. [source]