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Delay differential equations

Stavroulakis, I. P., Stavroulakis, I. P.
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The Spectrum of Delay Differential Equations with Large Delay

SIAM Journal on Mathematical Analysis, 2011
We show that the spectrum of linear delay differential equations with large delay splits into two different parts. One part, called the strong spectrum, converges to isolated points when the delay parameter tends to infinity. The other part, called the pseudocontinuous spectrum, accumulates near criticality and converges after rescaling to a set of ...
Serhiy Yanchuk
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Fuzzy delay differential equations

Fuzzy Optimization and Decision Making, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vasile Lupulescu, Umber Abbas
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Metastability for delayed differential equations

Physical Review E, 1999
In systems at phase transitions, two phases of the same substance may coexist for a long time before one of them dominates. We show that a similar phenomenon occurs in systems with delayed feedback, where short-term stable oscillatory patterns can also have very long lifetimes before vanishing into constant or periodic steady states.
C, Grotta-Ragazzo, K, Pakdaman, C P, Malta   +2 more
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HOPF BIFURCATION OF A DELAYED DIFFERENTIAL EQUATION

International Journal of Bifurcation and Chaos, 2007
In this paper, we study Hopf bifurcation of a second-order nonlinear differential equation with time delay by using the Lyapunov–Schmidt reduction. The approximate analytical expressions of the periodic solutions bifurcated from the trivial solution are given. We also discuss the stability of these periodic solutions. The numerical simulations line up
Qian Guo 0002, Changpin Li
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Delay differential equations

2012
In this chapter we study general non-autonomous delay differential equations of the form $$\dot{x}(t) = F(t,x(t),x(t - \rho (t))).$$ Our intention is to demonstrate how pullback attractors can be used to investigate the behaviour of such models.
Alexandre N. Carvalho, José A. Langa, James C. Robinson   +2 more
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Delays and Differential Delay Equations

1998
Mathematically speaking, the most important tools used by the chemical kineticist to study chemical reactions like the ones we have been considering are sets of coupled, first-order, ordinary differential equations that describe the changes in time of the concentrations of species in the system, that is, the rate laws derived from the Law of Mass ...
Irving R. Epstein, John A. Pojman
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Perturbations and Delays in Differential Equations

SIAM Journal on Applied Mathematics, 1975
In this paper we present a number of results on perturbations of second order differential equations of the form $x'' + f( x )h( {x'} )x' + g( x ) = 0$. This is accomplished by constructing a variety of Lyapunov functions. We then show how these Lyapunov functions can be converted to Lyapunov functionals for the delay equation $x'' + f( x )h( {x'} )x' +
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Analytic Solutions of Delay-Differential Equations

Journal of Dynamics and Differential Equations, 2021
The paper investigates analyticity of solutions to delay equations, which are defined (at least) on an interval of the form \( J = (- \infty, \gamma]\), given that the functions in the equation are analytic. An example is the equation \(\dot y (t) = g(y(t-1)) + \varepsilon \sin(t^2)\).
John Mallet-Paret, Roger D. Nussbaum
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Delay Differential Equations

2010
Dynamical systems with delay (which we simply designate hereafter as delay dynamical systems or delay systems) are abundant in nature. They occur in a wide variety of physical, chemical, engineering, economic and biological systems and their networks. One can cite many examples where delay plays an important role.
M. Lakshmanan, D.V. Senthilkumar
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