Relevant bibliographies by topics / Delay differential equations (DDEs)

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Delay differential equations (DDEs)'

Author: Grafiati
Published: 7 June 2025
Last updated: 2 August 2025

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Journal articles on the topic "Delay differential equations (DDEs)"

1

Wahi, Pankaj, and Anindya Chatterjee. "Galerkin Projections for Delay Differential Equations." Journal of Dynamic Systems, Measurement, and Control 127, no. 1 (2004): 80–87. http://dx.doi.org/10.1115/1.1870042.

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We present a Galerkin projection technique by which finite-dimensional ordinary differential equation (ODE) approximations for delay differential equations (DDEs) can be obtained in a straightforward fashion. The technique requires neither the system to be near a bifurcation point, nor the delayed terms to have any specific restrictive form, or even the delay, nonlinearities, and/or forcing to be small. We show through several numerical examples that the systems of ODEs obtained using this procedure can accurately capture the dynamics of the DDEs under study, and that the accuracy of solutions
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Naveen Kashyap and Dr. B. V. Padamvar. "Differential Difference Equations in Trajectory Planning and Control for Differential Drive Robots: A Comprehensive Exploration." Journal of Advances in Science and Technology 21, no. 1 (2024): 35–42. http://dx.doi.org/10.29070/5c5t1x55.

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This paper provides a thorough investigation into the utilisation of differential difference equations (DDEs) for the purposes of trajectory planning and control in the context of differential drive four-wheeled robots. The inclusion of sensor and control delays is crucial when developing navigation strategies that are both resilient and efficient for robots functioning in dynamic environments. Differential delay equations (DDEs) provide a robust mathematical framework for representing the dynamics of such systems, facilitating precise and reliable path tracking. In order to demonstrate the ve
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Ahmad, M. D. Al-Eybani. "Solving Delay Differential Equations Using the Method of Steps." International Journal of Mathematics and Physical Sciences Research 13, no. 1 (2025): 46–49. https://doi.org/10.5281/zenodo.15366549.

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<strong>Abstract:</strong> Delay differential equations (DDEs) are a class of differential equations where the derivative of the unknown function at a given time depends not only on the current state but also on its values at previous times. These equations arise in numerous fields, including biology, engineering, and economics. Unlike ordinary differential equations (ODEs), DDEs incorporate time delays, making their solution more complex due to the need for a history function. A common form of a first-order linear DDE with a constant delay is: where &nbsp;is the unknown function, &nbsp;and &n
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Bachar, Mostafa. "Linearized Stability Analysis of Nonlinear Delay Differential Equations with Impulses." Axioms 13, no. 8 (2024): 524. http://dx.doi.org/10.3390/axioms13080524.

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This paper explores the linearized stability of nonlinear delay differential equations (DDEs) with impulses. The classical results on the existence of periodic solutions are extended from ordinary differential equations (ODEs) to DDEs with impulses. Furthermore, the classical results of linearized stability for nonlinear semigroups are generalized to periodic DDEs with impulses. A significant challenge arises from the need for a discontinuous initial function to obtain periodic solutions. To address this, first-kind discontinuous spaces R([a,b],Rn) are introduced for defining DDEs with impulse
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Jin, Gang, Houjun Qi, Zhanjie Li, Jianxin Han, and Hua Li. "A Method for Stability Analysis of Periodic Delay Differential Equations with Multiple Time-Periodic Delays." Mathematical Problems in Engineering 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/9490142.

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Delay differential equations (DDEs) are widely utilized as the mathematical models in engineering fields. In this paper, a method is proposed to analyze the stability characteristics of periodic DDEs with multiple time-periodic delays. Stability charts are produced for two typical examples of time-periodic DDEs about milling chatter, including the variable-spindle speed milling system with one-time-periodic delay and variable pitch cutter milling system with multiple delays. The simulations show that the results gained by the proposed method are in close agreement with those existing in the pa
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Ignatius, N. Njoseh, and J. Mamadu Ebimene. "Solving Delay Differential Equations By Elzaki Transform Method." Boson Journal of Modern Physics 3, no. 1 (2017): 214–19. https://doi.org/10.5281/zenodo.3969415.

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In this paper, we implement the Elzaki transform method for the solution of delay differential equations (DDEs). The method executes the DDEs by implementing its properties on the given DDE. Also, the method treats the nonlinear terms with a well posed formula. The method is easy to implement with high level of accuracy. Also, restricted transformations, perturbation, linearization or discretization are not recognized. The resulting numerical evidences show that the method converges favourably to the analytic solution. All computational frameworks are performed with maple 18 software.
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Zhu, Qunxi, Yifei Shen, Dongsheng Li, and Wei Lin. "Neural Piecewise-Constant Delay Differential Equations." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 8 (2022): 9242–50. http://dx.doi.org/10.1609/aaai.v36i8.20911.

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Continuous-depth neural networks, such as the Neural Ordinary Differential Equations (ODEs), have aroused a great deal of interest from the communities of machine learning and data science in recent years, which bridge the connection between deep neural networks and dynamical systems. In this article, we introduce a new sort of continuous-depth neural network, called the Neural Piecewise-Constant Delay Differential Equations (PCDDEs). Here, unlike the recently proposed framework of the Neural Delay Differential Equations (DDEs), we transform the single delay into the piecewise-constant delay(s
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Naseem, Tahir. "Reduce Differential Transform Method for Analytical Approximation of Fractional Delay Differential Equation." International Journal of Emerging Multidisciplinaries: Mathematics 1, no. 2 (2022): 104–23. http://dx.doi.org/10.54938/ijemdm.2022.01.2.35.

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The study of an entirely new class of differential equations known as delay differential equations or difference differential equations has resulted from the development and application of automatic control systems (DDEs). Time delays are virtually always present in any system that uses feedback control. Because it takes a finite amount of time to sense information and then react to it, a time delay is required. This exploration was carried out for the solution of fractional delay differential equations by using the reduced differential transform method. The results are presented in a series o
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LUZYANINA, TATYANA, and KOEN ENGELBORGHS. "COMPUTING FLOQUET MULTIPLIERS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS." International Journal of Bifurcation and Chaos 12, no. 12 (2002): 2977–89. http://dx.doi.org/10.1142/s0218127402006291.

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Floquet multipliers determine the local asymptotic stability of a periodic solution and, in the context of parameter dependence, determine also its bifurcations. This paper deals with numerical aspects of the computation of the Floquet multipliers for three classes of functional differential equations: ordinary differential equations (ODEs), differential equations with constant delay (DDEs) and differential equations with state-dependent delay (sd-DDEs). Using a collocation approach for computing periodic solutions, we obtain an approximation of the (corresponding) monodromy operator, a monodr
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Olaniyan, Adegoke Stephen, Moshood Tolulope Kazeem, Azeez Adebayo Aweda, and Oladayo Ibukunoluwa Oladimeji. "Numerical Solution of Delay Differential Equations with Heronian Implicit Runge-Kutta Method." International Journal of Research and Innovation in Applied Science IX, no. XII (2025): 326–30. https://doi.org/10.51584/ijrias.2024.912030.

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In recent years, there has been growing interest in the numerical solution of Delay Differential Equations (DDEs). This is due to the fact that DDEs provides a good means of modelling many phenomena in diverse application fields ranging from physical sciences, economy, medicine, education to electrodynamics. Hence, the increased attention in the numerical solutions to such problems becomes a necessity. The purpose of this study is to present a numerical method that uses a polynomial interpolating function when solving DDEs. In this paper, Heronian Implicit Runge-Kutta method is considered for
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Dissertations / Theses on the topic "Delay differential equations (DDEs)"

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Gallage, Roshini Samanthi. "Approximation Of Continuously Distributed Delay Differential Equations." OpenSIUC, 2017. https://opensiuc.lib.siu.edu/theses/2196.

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We establish a theorem on the approximation of the solutions of delay differential equations with continuously distributed delay with solutions of delay differential equations with discrete delays. We present numerical simulations of the trajectories of discrete delay differential equations and the dependence of their behavior for various delay amounts. We further simulate continuously distributed delays by considering discrete approximation of the continuous distribution.
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Taylor, S. Richard. "Probabilistic Properties of Delay Differential Equations." Thesis, University of Waterloo, 2004. http://hdl.handle.net/10012/1183.

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Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, <em>i. e. </em> in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the dynamics of ensembles (statistical mechanics) and systems with uncertainty in the initial conditions. It is also the basis of ergodic theory--the study of probabilistic invariants of dynamical systems--which provides one framework for understanding chaotic systems whose time evolutions are erratic and for practical purposes unpredictable.
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Berntson, B. K. "Integrable delay-differential equations." Thesis, University College London (University of London), 2017. http://discovery.ucl.ac.uk/1566618/.

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Delay-differential equations are differential-difference equations in which the derivatives and shifts are taken with respect to the same variable. This thesis is concerned with these equations from the perspective of the theory of integrable systems, and more specifically, Painlevé equations. Both the classical Painlevé equations and their discrete analogues can be obtained as deautonomizations of equations solved by two-parameter families of elliptic functions. In analogy with this paradigm, we consider autonomous delay-differential equations solved by elliptic functions, delay-differentia
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Allen, Brenda. "Non-smooth differential delay equations." Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.390472.

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Fontana, Gaia. "Traffic waves and delay differential equations." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21211/.

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Questo elaborato si pone l'obiettivo di studiare il problema del traffico, concentrandosi su un modello semplificato in cui i veicoli sono confinati su una circonferenza e la cui velocità è determinata dal modello optimal velocity. Il discorso si sviluppa su tre capitoli: nel primo viene presentato il modello optimal velocity per il flusso del traffico e si procede a uno studio della stabilità lineare attorno al punto di equilibrio stazionario. Nel secondo capitolo lo stesso modello viene studiato nel limite termodinamico per un numero infinito di veicoli. Si ricava una soluzione costituita
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Ron, Eyal [Verfasser]. "Hysteresis-Delay Differential Equations / Eyal Ron." Berlin : Freie Universität Berlin, 2016. http://d-nb.info/1121588026/34.

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Zhang, Wenkui. "Numerical analysis of delay differential and integro-differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0011/NQ42489.pdf.

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Hines, Gwendolen. "Dependence of the attractor on the delay for delay-differential equations." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/28954.

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Bahar, Arifah. "Applications of stochastic differential equations and stochastic delay differential equations in population dynamics." Thesis, University of Strathclyde, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.415294.

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Reiss, Markus. "Nonparametric estimation for stochastic delay differential equations." [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=964782480.

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Books on the topic "Delay differential equations (DDEs)"

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Erneux, Thomas. Applied delay differential equations. Springer, 2009.

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2

Arino, O., M. L. Hbid, and E. Ait Dads, eds. Delay Differential Equations and Applications. Springer Netherlands, 2006. http://dx.doi.org/10.1007/1-4020-3647-7.

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Joseph, Wiener, Hale J. K, and International Conference on Theory and Applications of Differential Equations (1991 : Edinburg, Texas), eds. Ordinary and delay differential equations. Longman Scientific & Technical, 1992.

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1947-, Arino Ovide, Hbid M. L, and Ait Dads E, eds. Delay differential equations and applications. Springer, 2006.

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Joseph, Wiener, Hale Jack K, and International Conference on Theory and Applications of Differential Equations (1991 : University of Texas Pan-American), eds. Ordinary and delay differential equations. Longman Scientific & Technical, 1992.

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6

Gil’, Michael I. Stability of Vector Differential Delay Equations. Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0577-3.

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Busenberg, Stavros, and Mario Martelli, eds. Delay Differential Equations and Dynamical Systems. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0083474.

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Hino, Yoshiyuki, Satoru Murakami, and Toshiki Naito. Functional Differential Equations with Infinite Delay. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0084432.

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Breda, Dimitri, Stefano Maset, and Rossana Vermiglio. Stability of Linear Delay Differential Equations. Springer New York, 2015. http://dx.doi.org/10.1007/978-1-4939-2107-2.

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Marino, Zennaro, ed. Numerical methods for delay differential equations. Clarendon Press, 2003.

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Book chapters on the topic "Delay differential equations (DDEs)"

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Breda, Dimitri, Stefano Maset, and Rossana Vermiglio. "TRACE-DDE: a Tool for Robust Analysis and Characteristic Equations for Delay Differential Equations." In Topics in Time Delay Systems. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02897-7_13.

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Lynch, Stephen. "Delay Differential Equations." In Dynamical Systems with Applications Using Mathematica®. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-61485-4_12.

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Cooke, Kennet L. "Delay Differential Equations." In Mathematics of Biology. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11069-6_1.

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Soetaert, Karline, Jeff Cash, and Francesca Mazzia. "Delay Differential Equations." In Solving Differential Equations in R. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28070-2_6.

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Grigoriev, Yurii N., Nail H. Ibragimov, Vladimir F. Kovalev, and Sergey V. Meleshko. "Delay Differential Equations." In Symmetries of Integro-Differential Equations. Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-90-481-3797-8_6.

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Rand, Richard. "Differential-Delay Equations." In Complex Systems. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-17593-0_3.

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Lynch, Stephen. "Delay Differential Equations." In Dynamical Systems with Applications using Python. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-78145-7_12.

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Carvalho, Alexandre N., José A. Langa, and James C. Robinson. "Delay differential equations." In Applied Mathematical Sciences. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4581-4_10.

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Flunkert, Valentin. "Delay Differential Equations." In Delay-Coupled Complex Systems. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20250-6_15.

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Lakshmanan, M., and D. V. Senthilkumar. "Delay Differential Equations." In Dynamics of Nonlinear Time-Delay Systems. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14938-2_1.

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Conference papers on the topic "Delay differential equations (DDEs)"

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Pyrkova, Anna Yu, Aida M. Seitaliyeva, Zhanerke E. Temirbekova, Gulzinat K. Ordabayeva, and Yekaterina A. Zuyeva. "Mathematical Model of Blood Pressure Regulation Using Delay Differential Equations." In 2025 8th International Conference on Circuits, Systems and Simulation (ICCSS). IEEE, 2025. https://doi.org/10.1109/iccss65911.2025.11081737.

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Yi, Sun, and Sangseok Yu. "Estimation of Time-Delays Using the Characteristic Roots of Delay Differential Equations." In ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control. ASMEDC, 2011. http://dx.doi.org/10.1115/dscc2011-5919.

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In this short paper, the preliminary result of a new method for estimation of time-delays of time-delay systems is presented. The presented method makes use of the Lambert W function, and is for scalar first-order delay differential equations (DDEs). Possible extension to general systems of DDEs and application to physical systems are also discussed.
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Butcher, Eric A., and Oleg A. Bobrenkov. "The Chebyshev Spectral Continuous Time Approximation for Periodic Delay Differential Equations." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86641.

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In this paper, the approximation technique proposed in [1] for converting a system of constant-coefficient delay differential equations (DDEs) into a system of ordinary differential equations (ODEs) using pseudospectral differencing is applied to both constant and periodic systems of DDEs. Specifically, the use of Chebyshev spectral collocation is proposed in order to obtain the “spectral accuracy” convergence behavior shown in [1]. The proposed technique is used to study the stability of first and second order constant coefficient DDEs with one or two fixed delays with or without cubic nonlin
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Fofana, M. S. "A Unified Framework for the Study of Periodic Solutions of Nonlinear Delay Differential Equations." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21617.

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Abstract Periodic solutions of delay differential equations (DDEs) splitting into stable and unstable branches are examined in an infinite-dimensional space for fixed and multiple time delays. The center manifold theorem and the classical Hopf bifurcation theorem for the study of periodic solutions of ordinary differential equations (ODEs) are employed to reduce the infinite-dimensional character of the DDEs to finite-dimensional ODEs. Using integral averaging method, the vector field of the ODEs is converted and averaged into amplitude a and phase φ relations. From these relations bifurcation
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Wahi, Pankaj, and Anindya Chatterjee. "Galerkin Projections for Delay Differential Equations." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48570.

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We present a Galerkin projection technique by which finite-dimensional ODE approximations for DDE’s can be obtained in a straightforward fashion. The technique requires neither the system to be near a bifurcation point, nor the delayed terms to have any specific restrictive form, nor even the delay, nonlinearities and/or forcing to be small. We show through several numerical examples that the systems of ODE’s obtained using this procedure can accurately capture the dynamics of the DDE’s under study, and that the accuracy of solutions increases with increasing numbers of shape functions used in
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Takács, Árpád, Eric A. Butcher, and Tamás Insperger. "The Magnus Expansion for Periodic Delay Differential Equations." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12304.

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In this paper, the application of the Magnus expansion on periodic time-delayed differential equations is proposed, where an approximation technique of Chebyshev Spectral Continuous Time Approximation (CSCTA) is first used to convert a system of delayed differential equations (DDEs) into a system of ordinary differential equations (ODEs), whose solution are then obtained via the Magnus expansion. The stability and time response of this approach are investigated on two examples and compared with known results in the literature.
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Yi, Sun, Patrick W. Nelson, and A. Galip Ulsoy. "Feedback Control Via Eigenvalue Assignment for Time Delayed Systems Using the Lambert W Function." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35711.

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In this paper, we consider the problem of feedback controller design via eigenvalue assignment for systems of linear delay differential equations (DDEs). Unlike ordinary differential equations (ODEs), DDEs have an infinite eigenspectrum and it is not feasible to assign all closed-loop eigenvalues. However, we can assign a critical subset of them using a solution to linear DDEs in terms of the matrix Lambert W function. The solution has an analytical form expressed in terms of the parameters of the DDE, and is similar to the state transition matrix in linear ODEs. Hence, one can extend controll
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Bobrenkov, Oleg A., Morad Nazari, and Eric A. Butcher. "On the Analysis of Periodic Delay Differential Equations With Discontinuous Distributed Delays." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47671.

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In this paper, the analysis of delay differential equations with periodic coefficients and discontinuous distributed delay is carried out through discretization by Chebyshev spectral continuous time approximation (ChSCTA). These features are introduced in the delayed Mathieu equation with discontinuous distributed delay used as an illustrative example. The efficiency of the process of stability analysis is improved by using shifted Chebyshev polynomials for computing the monodromy matrix, as well as the adaptive meshing of the parameter plane. An idea for a method for numerical integration of
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Butcher, Eric A., Venkatesh Deshmukh, and Ed Bueler. "Center Manifold Reduction of Periodic Delay Differential Systems." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34583.

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A technique for center manifold reduction of nonlinear delay differential equations (DDEs) with time-periodic coefficients is presented. Perturbation expansion converts the nonlinear response problem into solutions of a series of non-homogenous linear ordinary differential equations (ODEs) with time periodic coefficients. One set of linear non-homogenous ODEs is solved for each power of the perturbation parameter. Each ODE is solved by a Chebyshev spectral collocation method. Thus we compute a finite approximation to the nonlinear infinite-dimensional map for the DDE. Center manifold reduction
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Yi, Sun, Patrick W. Nelson, and A. Galip Ulsoy. "Chatter Stability Analysis Using the Matrix Lambert Function and Bifurcation Analysis." In ASME 2006 International Manufacturing Science and Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/msec2006-21130.

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We investigate the stability of the regenerative machine tool chatter problem, in a turning process modeled using delay differential equations (DDEs). An approach using the matrix Lambert function for the analytical solution to systems to delay differential equations is applied to this problem and compared with the result obtained using a bifurcation analysis. The Lambert function, known to be useful for solving scalar first order DDEs, has recently been extended to a matrix Lambert function approach to solve systems of DDEs. The essential advantage of the matrix Lambert approach is not only t
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Reports on the topic "Delay differential equations (DDEs)"

1

Gilsinn, David E. Approximating periodic solutions of autonomous delay differential equations. National Institute of Standards and Technology, 2006. http://dx.doi.org/10.6028/nist.ir.7375.

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