Relevant bibliographies by topics / Integral delay equations

Contents

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

Academic literature on the topic 'Integral delay equations'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 February 2022

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Journal articles on the topic "Integral delay equations"

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Burton, T. A. "Integral equations with a delay." Acta Mathematica Hungarica 72, no. 3 (1996): 233–42. http://dx.doi.org/10.1007/bf00050686.

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Gilsinn, David E., and Florian A. Potra. "Integral Operators and Delay Differential Equations." Journal of Integral Equations and Applications 18, no. 3 (September 2006): 297–336. http://dx.doi.org/10.1216/jiea/1181075393.

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Li, Xiaoxuan. "Volterra Integral Equations with Vanishing Delay." Applied and Computational Mathematics 4, no. 3 (2015): 152. http://dx.doi.org/10.11648/j.acm.20150403.18.

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Karakostas, George, I. P. Stavroulakis, and Yumei Wu. "Oscillations of Volterra integral equations with delay." Tohoku Mathematical Journal 45, no. 4 (1993): 583–605. http://dx.doi.org/10.2748/tmj/1178225851.

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Xu, Dao Yi. "Integro-differential equations and delay integral inequalities." Tohoku Mathematical Journal 44, no. 3 (1992): 365–78. http://dx.doi.org/10.2748/tmj/1178227303.

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Melchor-Aguilar, Daniel, Vladimir Kharitonov, and Rogelio Lozano. "Lyapunov-Krasovskii functionals for integral delay equations." IFAC Proceedings Volumes 36, no. 19 (September 2003): 23–28. http://dx.doi.org/10.1016/s1474-6670(17)33296-2.

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Yatsenko, Yuri. "Volterra integral equations with unknown delay time." Methods and Applications of Analysis 2, no. 4 (1995): 408–19. http://dx.doi.org/10.4310/maa.1995.v2.n4.a3.

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BRUNNER, H. "Fully Discrete Galerkin Method For Fredholm Integro-Differential Equations With Weakly Singular Kernels." Computational Methods in Applied Mathematics 8, no. 3 (2008): 207–22. http://dx.doi.org/10.2478/cmam-2008-0015.

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AbstractWe analyze the optimal superconvergence properties of piecewise polynomial collocation solutions on uniform meshes for Volterra integral and integrodifferential equations with multiple (vanishing) proportional delays. It is shown that for delay integro-differential equations the recently obtained optimal order is also attainable. For integral equations with multiple vanishing delays this is no longer true.
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Liang, Jin, and Ti-Jun Xiao. "Solutions to abstract integral equations and infinite delay evolution equations." Bulletin of the Belgian Mathematical Society - Simon Stevin 18, no. 5 (November 2011): 793–804. http://dx.doi.org/10.36045/bbms/1323787167.

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El-Sayed, Ahmed M. A., and Yasmin M. Y. Omar. "Chandrasekhar quadratic and cubic integral equations via Volterra-Stieltjes quadratic integral equation." Demonstratio Mathematica 54, no. 1 (January 1, 2021): 25–36. http://dx.doi.org/10.1515/dema-2021-0003.

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Abstract In this work, we study the existence of one and exactly one solution x ∈ C [ 0 , 1 ] x\in C\left[0,1] , for a delay quadratic integral equation of Volterra-Stieltjes type. As special cases we study a delay quadratic integral equation of fractional order and a Chandrasekhar cubic integral equation.
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Dissertations / Theses on the topic "Integral delay equations"

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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-differential extensions of the Painlevé equations, and the interrelations between these classes of equations. We develop a method to identify delay-differential equations that admit families of elliptic solutions with at least two degrees of parametric freedom and apply it to two natural 16-parameter families of delay-differential equations. Some of the resulting equations are related to known models including the differential-difference sine-Gordon equation and the Volterra lattice; the corresponding new solutions to these and other equations are constructed in a number of examples. Other equations we have identified appear to be new. Bäcklund transformations for the classical Painlevé equations provide a source of delay-differential Painlevé equations. These transformations were previously used to derive discrete Painlevé equations. We use similar methods to identify delay-differential equations with continuum limits to the first classical Painlevé equation. The equations we identify are solved by elliptic functions in particular limits corresponding to the autonomous limit of the classical first Painlevé equation.
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Rocha, Eugénio Alexandre Miguel. "Uma Abordagem Algébrica à Teoria de Controlo Não Linear." Doctoral thesis, Universidade de Aveiro, 2003. http://hdl.handle.net/10773/21444.

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Doutoramento em Matemática
Nesta tese de Doutoramento desenvolve-se principalmente uma abordagem algébrica à teoria de sistemas de controlo não lineares. No entanto, outros tópicos são também estudados. Os tópicos tratados são os seguidamente enunciados: fórmulas para sistemas de controlo sobre álgebras de Lie livres, estabilidade de um sistema de corpos rolantes, algoritmos para aritmética digital, e equações integrais de Fredholm não lineares. No primeiro e principal tópico estudam-se representações para as soluções de sistemas de controlo lineares no controlo. As suas trajetórias são representadas pelas chamadas séries de Chen. Estuda-se a representação formal destas séries através da introdução de várias álgebras não associativas e técnicas específicas de álgebras de Lie livres. Sistemas de coordenadas para estes sistemas são estudados, nomeadamente, coordenadas de primeiro tipo e de segundo tipo. Apresenta-se uma demonstração alternativa para as coordenadas de segundo tipo e obtêm-se expressões explícitas para as coordenadas de primeiro tipo. Estas últimas estão intimamente ligadas ao logaritmo da série de Chen que, por sua vez, tem fortes relações com uma fórmula designada na literatura por “continuous Baker-Campbell- Hausdorff formula”. São ainda apresentadas aplicações à teoria de funções simétricas não comutativas. É, por fim, caracterizado o mapa de monodromia de um campo de vectores não linear e periódico no tempo em relação a uma truncatura do logaritmo de Chen. No segundo tópico é estudada a estabilizabilidade de um sistema de quaisquer dois corpos que rolem um sobre o outro sem deslizar ou torcer. Constroem-se controlos fechados e dependentes do tempo que tornam a origem do sistema de dois corpos num sistema localmente assimptoticamente estável. Vários exemplos e algumas implementações em Maple°c são discutidos. No terceiro tópico, em apêndice, constroem-se algoritmos para calcular o valor de várias funções fundamentais na aritmética digital, sendo possível a sua implementação em microprocessadores. São também obtidos os seus domínios de convergência. No último tópico, também em apêndice, demonstra-se a existência e unicidade de solução para uma classe de equações integrais não lineares com atraso. O atraso tem um carácter funcional, mostrando-se ainda a diferenciabilidade no sentido de Fréchet da solução em relação à função de atraso.
In this PhD thesis several subjects are studied regarding the following topics: formulas for nonlinear control systems on free Lie algebras, stabilizability of nonlinear control systems, digital arithmetic algorithms, and nonlinear Fredholm integral equations with delay. The first and principal topic is mainly related with a problem known as the continuous Baker-Campbell-Hausdorff exponents. We propose a calculus to deal with formal nonautonomous ordinary differential equations evolving on the algebra of formal series defined on an alphabet. We introduce and connect several (non)associative algebras as Lie, shuffle, zinbiel, pre-zinbiel, chronological (pre-Lie), pre-chronological, dendriform, D-I, and I-D. Most of those notions were also introduced into the universal enveloping algebra of a free Lie algebra. We study Chen series and iterated integrals by relating them with nonlinear control systems linear in control. At the heart of all the theory of Chen series resides a zinbiel and shuffle homomorphism that allows us to construct a purely formal representation of Chen series on algebras of words. It is also given a pre-zinbiel representation of the chronological exponential, introduced by A.Agrachev and R.Gamkrelidze on the context of a tool to deal with nonlinear nonautonomous ordinary differential equations over a manifold, the so-called chronological calculus. An extensive description of that calculus is made, collecting some fragmented results on several publications. It is a fundamental tool of study along the thesis. We also present an alternative demonstration of the result of H.Sussmann about coordinates of second kind using the mentioned tools. This simple and comprehensive proof shows that coordinates of second kind are exactly the image of elements of the dual basis of a Hall basis, under the above discussed homomorphism. We obtain explicit expressions for the logarithm of Chen series and the respective coordinates of first kind, by defining several operations on a forest of leaf-labelled trees. It is the same as saying that we have an explicit formula for the functional coefficients of the Lie brackets on a continuous Baker-Campbell-Hausdorff-Dynkin formula when a Hall basis is used. We apply those formulas to relate some noncommutative symmetric functions, and we also connect the monodromy map of a time-periodic nonlinear vector field with a truncation of the Chen logarithm. On the second topic, we study any system of two bodies rolling one over the other without twisting or slipping. By using the Chen logarithm expressions, the monodromy map of a flow and Lyapunov functions, we construct time-variant controls that turn the origin of a control system linear in control into a locally asymptotically stable equilibrium point. Stabilizers for control systems whose vector fields generate a nilpotent Lie algebra with degree of nilpotency · 3 are also given. Some examples are presented and Maple°c were implemented. The third topic, on appendix, concerns the construction of efficient algorithms for Digital Arithmetic, potentially for the implementation in microprocessors. The algorithms are intended for the computation of several functions as the division, square root, sines, cosines, exponential, logarithm, etc. By using redundant number representations and methods of Lyapunov stability for discrete dynamical systems, we obtain several algorithms (that can be glued together into an algorithm for parallel execution) having the same core and selection scheme in each iteration. We also prove their domains of convergence and discuss possible extensions. The last topic, also on appendix, studies the set of solutions of a class of nonlinear Fredholm integral equations with general delay. The delay is of functional character modelled by a continuous lag function. We ensure existence and uniqueness of a continuous (positive) solution of such equation. Moreover, under additional conditions, it is obtained the Fr´echet differentiability of the solution with respect to the lag function.
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Adamík, Pavel. "Řízení dynamických systémů v reálném čase." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2009. http://www.nusl.cz/ntk/nusl-236759.

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This thesis focuses on the methodology of controlling dynamic systems in real time. It contents a review of the control theory basis and the elementary base of regulators construction. Then the list of matemathic formulaes follows as well as the math basis for the system simulations using a difeerential count and the problem of difeerential equations solving. Furthermore, there is a systematic approach to the design of general regulator enclosed, using modern simulation techniques. After the results confirmation in the Matlab system, the problematics of transport delay & quantization modelling follow.
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LI, ZHONG-FEN, and 李中芬. "Oscillations of delay Volterra- Stieltjes integral equations." Thesis, 1992. http://ndltd.ncl.edu.tw/handle/26684478027150829980.

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Lamzouri, Youness. "Sur la distribution des valeurs de la fonction zêta de Riemann et des fonctions L au bord de la bande critque." Thèse, 2009. http://hdl.handle.net/1866/6626.

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Books on the topic "Integral delay equations"

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Morawetz, Klaus. Classical Kinetic Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0003.

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The classical non-ideal gas shows that the two original concepts of the pressure based of the motion and the forces have eventually developed into drift and dissipation contributions. Collisions of realistic particles are nonlocal and non-instant. A collision delay characterizes the effective duration of collisions, and three displacements, describe its effective non-locality. Consequently, the scattering integral of kinetic equation is nonlocal and non-instant. The non-instant and nonlocal corrections to the scattering integral directly result in the virial corrections to the equation of state. The interaction of particles via long-range potential tails is approximated by a mean field which acts as an external field. The effect of the mean field on free particles is covered by the momentum drift. The effect of the mean field on the colliding pairs causes the momentum and the energy gains which enter the scattering integral and lead to an internal mechanism of energy conversion. The entropy production is shown and the nonequilibrium hydrodynamic equations are derived. Two concepts of quasiparticle, the spectral and the variational one, are explored with the help of the virial of forces.
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Morawetz, Klaus. Properties of Non-Instant and Nonlocal Corrections. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0014.

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The derived nonlocal and non-instant shifts are discussed with respect to various symmetries and gauges. The classical counterparts are derived and found in agreement with the expected phenomenological ones from chapter 3. The explicit forms of the hard-sphere like offsets and the delay time in terms of the scattering phase shifts are calculated and discussed on the example of nuclear collision. The numerical results reveal an interesting inside into the microscopic correlations developed in dependence on the scattering angle and scattering energy. The just-accomplished derivation of the nonlocal scattering integrals is far from being intuitive. We have reached our task, the kinetic equation, being guided by nothing but systematic implementation of the quasiclassical approximation and the limit of small scattering rates.
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Koch, Christof. Biophysics of Computation. Oxford University Press, 1998. http://dx.doi.org/10.1093/oso/9780195104912.001.0001.

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Neural network research often builds on the fiction that neurons are simple linear threshold units, completely neglecting the highly dynamic and complex nature of synapses, dendrites, and voltage-dependent ionic currents. Biophysics of Computation: Information Processing in Single Neurons challenges this notion, using richly detailed experimental and theoretical findings from cellular biophysics to explain the repertoire of computational functions available to single neurons. The author shows how individual nerve cells can multiply, integrate, or delay synaptic inputs and how information can be encoded in the voltage across the membrane, in the intracellular calcium concentration, or in the timing of individual spikes. Key topics covered include the linear cable equation; cable theory as applied to passive dendritic trees and dendritic spines; chemical and electrical synapses and how to treat them from a computational point of view; nonlinear interactions of synaptic input in passive and active dendritic trees; the Hodgkin-Huxley model of action potential generation and propagation; phase space analysis; linking stochastic ionic channels to membrane-dependent currents; calcium and potassium currents and their role in information processing; the role of diffusion, buffering and binding of calcium, and other messenger systems in information processing and storage; short- and long-term models of synaptic plasticity; simplified models of single cells; stochastic aspects of neuronal firing; the nature of the neuronal code; and unconventional models of sub-cellular computation. Biophysics of Computation: Information Processing in Single Neurons serves as an ideal text for advanced undergraduate and graduate courses in cellular biophysics, computational neuroscience, and neural networks, and will appeal to students and professionals in neuroscience, electrical and computer engineering, and physics.
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Book chapters on the topic "Integral delay equations"

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Karafyllis, Iasson, and Miroslav Krstic. "Systems Described by Integral Delay Equations." In Predictor Feedback for Delay Systems: Implementations and Approximations, 229–50. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-42378-4_7.

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Lunel, Sjoerd M. Verduyn. "Spectral theory for delay equations." In Systems, Approximation, Singular Integral Operators, and Related Topics, 465–507. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8362-7_19.

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Agarwal, Ravi P., Donal O’Regan, and Patricia J. Y. Wong. "Delay Boundary Value Problems." In Positive Solutions of Differential, Difference and Integral Equations, 110–18. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-015-9171-3_10.

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Ignatyev, Alexander O. "Asymptotic Stability in Functional Differential Equations with Delay." In Integral Methods in Science and Engineering, 97–102. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-0-8176-8184-5_17.

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Bresch-Pietri, Delphine, and Nicolas Petit. "Implicit Integral Equations for Modeling Systems with a Transport Delay." In Recent Results on Time-Delay Systems, 3–21. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-26369-4_1.

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Duman, Oktay. "Error Estimation for Approximate Solutions of Delay Volterra Integral Equations." In Frontiers in Functional Equations and Analytic Inequalities, 585–97. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28950-8_29.

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Castro, L. P., and A. Ramos. "Hyers–Ulam and Hyers–Ulam–Rassias Stability of Volterra Integral Equations with Delay." In Integral Methods in Science and Engineering, Volume 1, 85–94. Boston: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4899-2_9.

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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, 251–92. Dordrecht: Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-90-481-3797-8_6.

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Rajiv Ganthi, C., and P. Muthukumar. "Approximate Controllability of Fractional Stochastic Integral Equation with Finite Delays in Hilbert Spaces." In Mathematical Modelling and Scientific Computation, 302–9. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28926-2_32.

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"Volterra Integral Processes with Delay: Necessary Optimality Conditions." In Volterra Equations and Applications, 459–66. CRC Press, 2000. http://dx.doi.org/10.1201/9781482287424-55.

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Conference papers on the topic "Integral delay equations"

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Li, Hongfei, and Lijun Zhang. "Stability of Difference-Integral Delay Equations." In 2020 39th Chinese Control Conference (CCC). IEEE, 2020. http://dx.doi.org/10.23919/ccc50068.2020.9188694.

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Yuanqu Lin and Daniel S. Weile. "Finite difference delay modeling for two-dimenisional time domain integral equations." In 2009 IEEE Antennas and Propagation Society International Symposium (APSURSI). IEEE, 2009. http://dx.doi.org/10.1109/aps.2009.5171923.

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Rezounenko, Alexander. "Stability of positive solutions of local partial differential equations with a nonlinear integral delay term." In The 8'th Colloquium on the Qualitative Theory of Differential Equations. Szeged: Bolyai Institute, SZTE, 2007. http://dx.doi.org/10.14232/ejqtde.2007.7.17.

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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 equations of the form ℑ(a, φ) = 0 for the solution branches are derived.
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Ren, Chuanbo, and Xiangtao Tian. "Solution for Dynamics Equations of Control Systems with Time-delay by Precise Integral Algorithm." In Sixth International Conference on Intelligent Systems Design and Applications. IEEE, 2006. http://dx.doi.org/10.1109/isda.2006.253823.

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Manjuram, R., and V. Muthulakshmi. "Oscillatory behavior of damped second-order nonlinear delay differential equations with riemann-stieltjes integral." In PROCEEDINGS OF INTERNATIONAL CONFERENCE ON ADVANCES IN MATERIALS RESEARCH (ICAMR - 2019). AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0017693.

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Butcher, Eric A., Haitao Ma, Ed Bueler, Victoria Averina, and Zsolt Szabo. "Stability Analysis of Parametrically Excited Systems With Time-Delay." 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-48574.

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This paper presents a new technique for studying the stability properties of parametrically excited dynamic systems with time delay modeled by delay-differential equations (DDEs) with time-periodic parameters. By employing a shifted Chebyshev polynomial approximation in each time interval with length equal to the delay period, the dynamic system can be reduced to a set of linear difference equations for the Chebyshev expansion coefficients of the state vector in the previous and current intervals. This defines a linear map which is the “infinite-dimensional Floquet transition matrix U”. Two different formulas for the computation of the approximate U, whose size is determined by the number of polynomials employed, are given. The first one, which results in a numerical stability matrix, uses the direct integral form of the original system in state space form while the second, which can give a symbolic stability matrix in terms of parameters, uses a convolution integral (variation of parameters) formulation. An extension of the method to the case where the delay and parametric periods are commensurate is also available. Numerical and symbolic stability charts are produced for several examples of time-periodic DDEs, including the delayed Mathieu equation and a model for regenerative chatter in impedance-modulated turning. The results indicate that this method is a effective way to study the stability of periodic DDEs.
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Xiaobo Wang and D. S. Weile. "Finite difference delay modeling with runge-kutta methods for the discretization of time domain integral equations." In 2010 IEEE International Symposium Antennas and Propagation and CNC-USNC/URSI Radio Science Meeting. IEEE, 2010. http://dx.doi.org/10.1109/aps.2010.5561956.

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Weile, D. S. "A hybrid galerkin/finite difference delay modeling method for the time domain integral equations of electromagnetics." In 2013 International Conference on Electromagnetics in Advanced Applications (ICEAA). IEEE, 2013. http://dx.doi.org/10.1109/iceaa.2013.6632224.

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Xiaobo Wang, Daniel S. Weile, and Peter Monk. "A finite difference delay estimation approach to the discretization of the time domain integral equations of electromagnetics." In 2007 IEEE Antennas and Propagation Society International Symposium. IEEE, 2007. http://dx.doi.org/10.1109/aps.2007.4396562.

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