Discretisation of an infinite delay equation [PDF]
Mathematics of Computation, 2006 In this paper, a Banach phase space containing BC(-∞,0] and contained in C(-∞,0] is defined with which existence of a solution and convergence of a discrete scheme are proved for an infinite delay differential equation.
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Reduction theories elucidate the origins of complex biological rhythms generated by interacting delay-induced oscillations. [PDF]
PLoS ONE, 2011 Time delay is known to induce sustained oscillations in many biological systems such as electroencephalogram (EEG) activities and gene regulations. Furthermore, interactions among delay-induced oscillations can generate complex collective rhythms, which ...
Ikuhiro Yamaguchi +4 more
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Linearization for Difference Equations with Infinite Delay
, 2023 In this article, we construct a conjugacy map for a linear difference equation with infinite delay and corresponding nonlinear perturbation. We also prove that the conjugacy map is one-one with some additional conditions. As an application of our result, we show that the cases of (uniform) exponential dichotomy follow from our result.
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Non-Markovian Dynamics of a Qubit Due to Single-Photon Scattering in a Waveguide [PDF]
, 2018 We investigate the open dynamics of a qubit due to scattering of a single photon in an infinite or semi-infinite waveguide. Through an exact solution of the time-dependent multi-photon scattering problem, we find the qubit's dynamical map.
Baranger, Harold U. +2 more
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Oscillation of equations with an infinite distributed delay
Computers & Mathematics with Applications, 2010 AbstractFor the equation with a finite or infinite distributed delay ẋ(t)+∫−∞tx(s)dsR(t,s)=0 the existence of nonoscillatory solutions is studied. A general comparison theorem is obtained which allows to compare oscillation properties of equations with concentrated delays to integrodifferential equations.
Leonid Berezansky, Elena Braverman
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Stability and Boundedness of Stochastic Volterra Integrodifferential Equations with Infinite Delay
Journal of Applied Mathematics, 2013 We make the first attempt to discuss stability and boundedness of solutions to stochastic Volterra integrodifferential equations with infinite delay (IDSVIDEs).
Chunmei Zhang, Wenxue Li, Ke Wang
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Imaginary Potential as a Counter of Delay Time for Wave Reflection from a 1D Random Potential [PDF]
, 1999 We show that the delay time distribution for wave reflection from a one-dimensional random potential is related directly to that of the reflection coefficient, derived with an arbitrarily small but uniform imaginary part added to the random potential ...
A. Comtet +23 more
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Approximate Controllability of Fractional Neutral Evolution Equations in Banach Spaces
Abstract and Applied Analysis, 2013 We discuss the approximate controllability of semilinear fractional neutral differential systems with infinite delay under the assumptions that the corresponding linear system is approximately controllable.
N. I. Mahmudov
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Time-delayed feedback control of the Dicke-Hepp-Lieb superradiant quantum phase transition [PDF]
, 2014 We apply the time-delayed Pyragas control scheme to the dissipative Dicke model via a modulation of the atom-field-coupling. The feedback creates an infinite sequence of non-equilibrium phases with fixed points and limit cycles in the primary ...
Brandes, Tobias +3 more
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Global convergence of successive approximations of the Darboux problem for partial functional differential equations with infinite delay [PDF]
Opuscula Mathematica, 2014 We consider the Darboux problem for the hyperbolic partial functional differential equation with infinite delay. We deal with generalized (in the "almost everywhere" sense) solutions of this problem.
Tomasz Człapiński
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