Results 211 to 220 of about 875,467 (271)

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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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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Bifurcation delay in a delay differential equation

Nonlinear Analysis: Theory, Methods & Applications, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Miyazaki, R., Tchizawa, K.
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Stability of Solutions of Delay Differential Equations

Siberian Advances in Mathematics, 2023
Summary: In the present article, we consider a class of systems of linear differential equations with infinite distributed delay and periodic coefficients. We use the Lyapunov-Krasovskii functional and obtain sufficient conditions for exponential stability of the zero solution, find conditions on perturbation of the coefficients of the system that ...
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The delay differential equation

Mathematika, 1986
The usual method of dealing with delay differential equations such asis the method of steps [1, 2]. In this, y(x) is assumed to be known for − α < x < 0, thereby defining over 0 < x < α. As a result of integration, the value of y is now known over 0 < x < α, and the integration proceeds thereon by a succession of steps.
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Delayed Differential Equations

2014
Matematik olaylarıx'(t) = f(t, x(t ...
GÖZÜKIZIL, Ömer, Şencan, Huri
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Differential-Delay Equations

2011
Periodic motions in DDE (Differential-Delay Equations) are typically created in Hopf bifurcations. In this chapter we examine this process from several points of view. Firstly we use Lindstedt’s perturbation method to derive the Hopf Bifurcation Formula, which determines the stability of the periodic motion.
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Construction of differential equation approximations to delay differential equations

Applicable Analysis, 1988
A constructive method is presented for obtaining differential equation approximations to general functional delay differential equations. It is shown that the approximating differential equation systems can be used to determine the stability of the functional differential ...
Stavros Busenberg, L. Thomas hill
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Delay and Differential Equations

Delay and Differential Equations, 1992
A. M. Fink, Richard K. Miller, Wolfgang Kliemann   +2 more
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