Generalized LMMSE Filtering with Out-of-Sequence Observations in Arbitrary Constant Delay

In this paper we apply existing numerical methods for bifurcation analysis of delay differential equations with constant delay to equations with state-dependent delay. In particular, we study the computation, continuation and stability analysis of steady state solutions and periodic solutions. We collect the relevant theory and describe open theoretical problems in the context of bifurcation analysis. We present computational results for two examples and compare with analytical results whenever possible.

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Steady-state periodic and rotational motions in perturbed, significantly nonlinear and almost conservative systems with one degree of freedom, in the case of an arbitrary constant deviation of the argument

Journal of Applied Mathematics and Mechanics ◽

10.1016/0021-8928(68)90154-8 ◽

1968 ◽

Vol 32 (1) ◽

pp. 114-121

Author(s):

L.L. Akulenko

Keyword(s):

Steady State ◽

Arbitrary Constant ◽

Degree Of Freedom ◽

Conservative Systems ◽

Rotational Motions ◽

Constant Deviation

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Strong convergence of the semi-implicit Euler method for nonlinear stochastic Volterra integral equations with constant delay

Applied Mathematics and Computation ◽

10.1016/j.amc.2018.10.025 ◽

2019 ◽

Vol 348 ◽

pp. 385-398 ◽

Cited By ~ 1

Author(s):

Jianfang Gao ◽

Hui Liang ◽

Shufang Ma

Keyword(s):

Strong Convergence ◽

Integral Equations ◽

Euler Method ◽

Volterra Integral Equations ◽

Constant Delay ◽

Implicit Euler Method

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Temperature Distribution in a Cylindrical Rod Moving From a Chamber at One Temperature to a Chamber at Another Temperature

Journal of Heat Transfer ◽

10.1115/1.3687119 ◽

1964 ◽

Vol 86 (2) ◽

pp. 265-270 ◽

Cited By ~ 4

Author(s):

G. Horvay ◽

M. Dacosta

Keyword(s):

Heat Transfer ◽

Temperature Distribution ◽

Arbitrary Constant ◽

Families Of Curves ◽

Special Cases ◽

Method Of Solution ◽

Lower Chamber ◽

Higher Temperature ◽

Hopf Method ◽

The Heat Transfer Coefficient

When an infinitely long cylindrical rod travels from a chamber at one temperature ϑa to a chamber (insulated from the first) at a higher temperature ϑf, then heat will leak out along the rod from the second chamber to the first, whose amount decreases as the speed of the rod increases. Using the Wiener-Hopf method of solution, we determine the temperature distribution in the rod for the case where in the second chamber the heat-transfer coefficient h+ is infinite, while in the first chamber it has an arbitrary constant value h. Families of curves illustrate the temperature distribution in the two special cases where h = ∞ (isothermal boundary conditions in lower chamber) and where h = 0 (rod is insulated in lower chamber).

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Periodic Solutions for a Class of Functional Differential Equations with State-Dependent Delay Close to Zero

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202503002738 ◽

2003 ◽

Vol 13 (06) ◽

pp. 807-841 ◽

Cited By ~ 6

Author(s):

R. Ouifki ◽

M. L. Hbid

Keyword(s):

Differential Equation ◽

Hopf Bifurcation ◽

Periodic Solutions ◽

Functional Differential Equations ◽

Delay Equation ◽

Constant Delay ◽

State Dependent ◽

State Dependent Delay ◽

Existence Of Periodic Solutions ◽

Functional Differential

The purpose of the paper is to prove the existence of periodic solutions for a functional differential equation with state-dependent delay, of the type [Formula: see text] Transforming this equation into a perturbed constant delay equation and using the Hopf bifurcation result and the Poincaré procedure for this last equation, we prove the existence of a branch of periodic solutions for the state-dependent delay equation, bifurcating from r ≡ 0.

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