Numerical approaches for state-dependent neutral delay equations with discontinuities

2014 ◽  
Vol 95 ◽  
pp. 2-12 ◽  
Author(s):  
Nicola Guglielmi ◽  
Ernst Hairer
Keyword(s):  
Delay Equations ◽  
Neutral Delay ◽  
State Dependent ◽  
Numerical Approaches

State-dependent neutral delay equations from population dynamics

2014 ◽  
Vol 69 (4) ◽  
pp. 1027-1056 ◽  
Author(s):  
M. V. Barbarossa ◽  
K. P. Hadeler ◽  
C. Kuttler
Keyword(s):  
Population Dynamics ◽  
Delay Equations ◽  
Neutral Delay ◽  
State Dependent

Identification of Parameters in Hereditary Systems

1995 ◽  
Author(s):  
Ferenc Hartung ◽  
Janos Turi ◽  
Terry L. Herdman
Keyword(s):  
Parameter Identification ◽  
Delay Equations ◽  
Neutral Equations ◽  
Piecewise Constant Arguments ◽  
Piecewise Constant ◽  
Identification Of Parameters ◽  
State Dependent ◽  
Identification Technique ◽  
Numerical Performance

Abstract In this paper we study the numerical performance of a parameter identification technique, based on approximation by equations with piecewise constant arguments, on various classes of hereditary systems. The examples considered here include delay equations with state-dependent delays and neutral equations.

scholarly journals Multiple periodic solutions for a class of second-order nonlinear neutral delay equations

2006 ◽  
Vol 2006 ◽  
pp. 1-9 ◽  
Author(s):  
Xiao-Bao Shu ◽  
Yuan-Tong Xu
Keyword(s):  
Periodic Solutions ◽  
Index Theory ◽  
Second Order ◽  
Delay Equations ◽  
Group Index ◽  
Neutral Delay ◽  
Variational Structure ◽  
Multiple Periodic Solutions ◽  
T Tau

By means of a variational structure andZ2-group index theory, we obtain multiple periodic solutions to a class of second-order nonlinear neutral delay equations of the formx″(t−τ)+λ(t)f(t,x(t),x(t−τ),x(t−2τ))=x(t),λ(t)>0,τ>0.

scholarly journals Variational Methods for Almost Periodic Solutions of a Class of Neutral Delay Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
M. Ayachi ◽  
J. Blot
Keyword(s):  
Variational Methods ◽  
Periodic Solutions ◽  
Delay Equations ◽  
Delay Equation ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Neutral Delay ◽  
Density Result

We provide new variational settings to study the a.p. (almost periodic) solutions of a class of nonlinear neutral delay equations. We extend Shu and Xu (2006) variational setting for periodic solutions of nonlinear neutral delay equation to the almost periodic settings. We obtain results on the structure of the set of the a.p. solutions, results of existence of a.p. solutions, results of existence of a.p. solutions, and also a density result for the forced equations.

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