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Relevant bibliographies by topics / Ordinary Differential Equations, Difference Equations and Dynamical Systems

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Dissertations / Theses
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Academic literature on the topic 'Ordinary Differential Equations, Difference Equations and Dynamical Systems'

Author: Grafiati

Published: 4 June 2021

Last updated: 19 February 2023

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Journal articles on the topic "Ordinary Differential Equations, Difference Equations and Dynamical Systems"

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Iwasa, Masatomo. "Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups." Journal of Applied Mathematics 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/601657.

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Lie group analysis has been applied to singular perturbation problems in both ordinary differential and difference equations and has allowed us to find the reduced dynamics describing the asymptotic behavior of the dynamical system. The present study provides an extended method that is also applicable to partial differential equations. The main characteristic of the extended method is the restriction of the manifold by some constraint equations on which we search for a Lie symmetry group. This extension makes it possible to find a partial Lie symmetry group, which leads to a reduced dynamics d

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Khan, Najeeb Alam, and Fatima Riaz. "Analytical and numerical results of fractional differential-difference equations." Acta Universitatis Sapientiae, Mathematica 7, no. 2 (2015): 186–99. http://dx.doi.org/10.1515/ausm-2015-0012.

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Abstract In this paper, we examine the fractional differential-difference equation (FDDE) by employing the proposed sensitivity approach (SA) and Adomian transformation method (ADTM). In SA the nonlinear differential-difference equation is converted to infinite linear equations which have a wide criterion to solve for the analytical solution. By ADTM, the FDDE is converted into ordinary differential-difference equation that can be solved. We test both the techniques through some test problems which are arising in nonlinear dynamical systems and found that ADTM is equivalently appropriate and s

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Wang, Xiaofeng, and Xiaohe Chen. "Derivative-Free Kurchatov-Type Accelerating Iterative Method for Solving Nonlinear Systems: Dynamics and Applications." Fractal and Fractional 6, no. 2 (2022): 59. http://dx.doi.org/10.3390/fractalfract6020059.

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Two novel Kurchatov-type first-order divided difference operators were designed, which were used for constructing the variable parameter of three derivative-free iterative methods. The convergence orders of the new derivative-free methods are 3, (5+17)/2≈4.56 and 5. The new derivative-free iterative methods with memory were applied to solve nonlinear ordinary differential equations (ODEs) and partial differential equations (PDEs) in numerical experiments. The dynamical behavior of our new methods with memory was studied by using dynamical plane. The dynamical planes showed that our methods had

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Andrianov, Igor, Galina Starushenko, Sergey Kvitka та Lelya Khajiyeva. "The Verhulst-Like Equations: Integrable OΔE and ODE with Chaotic Behavior". Symmetry 11, № 12 (2019): 1446. http://dx.doi.org/10.3390/sym11121446.

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In this paper, we study various variants of Verhulst-like ordinary differential equations (ODE) and ordinary difference equations (O Δ E). Usually Verhulst ODE serves as an example of a deterministic system and discrete logistic equation is a classic example of a simple system with very complicated (chaotic) behavior. In our paper we present examples of deterministic discretization and chaotic continualization. Continualization procedure is based on Padé approximants. To correctly characterize the dynamics of obtained ODE we measured such characteristic parameters of chaotic dynamical systems

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Iwasa, M. "Reduction of Dynamics with Lie Group Analysis." Advances in Mathematical Physics 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/505281.

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This paper is mainly a review concerning singular perturbation methods by means of Lie group analysis which has been presented by the author. We make use of a particular type of approximate Lie symmetries in those methods in order to construct reduced systems which describe the long-time behavior of the original dynamical system. Those methods can be used in analyzing not only ordinary differential equations but also difference equations. Although this method has been mainly used in order to derive asymptotic behavior, when we can find exact Lie symmetries, we succeed in construction of exact

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Klamka, J. "Controllability of dynamical systems. A survey." Bulletin of the Polish Academy of Sciences: Technical Sciences 61, no. 2 (2013): 335–42. http://dx.doi.org/10.2478/bpasts-2013-0031.

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Abstract The main objective of this article is to review the major progress that has been made on controllability of dynamical systems over the past number of years. Controllability is one of the fundamental concepts in the mathematical control theory. This is a qualitative property of dynamical control systems and is of particular importance in control theory. A systematic study of controllability was started at the beginning of sixties in the last century, when the theory of controllability based on the description in the form of state space for both time-invariant and time-varying linear co

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Ali, Ishtiaq, Ghulam Rasool, and Saleh Alrashed. "Numerical simulations of reaction–diffusion equations modeling prey–predator interaction with delay." International Journal of Biomathematics 11, no. 04 (2018): 1850054. http://dx.doi.org/10.1142/s1793524518500547.

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To model biological systems one often uses ordinary and partial differential equations. These equations can be quite good at approximating observed behavior, but they suffer from the downfall of containing many parameters, often signifying quantities which cannot be determined experimentally. For the better understanding of complicated phenomena, the delay differential equation approach to model such phenomena is becoming more and more essential to capture the rich variety of dynamics observed in natural systems. In this study, we investigated numerically the influence of delay on the dynamics

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Alhelfi, Ali, and Bengt Ake Sunden. "A new formulation and analysis of a collapsing bubble with different content in a liquid induced during acoustic cavitation." International Journal of Numerical Methods for Heat & Fluid Flow 26, no. 6 (2016): 1729–46. http://dx.doi.org/10.1108/hff-02-2015-0044.

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Purpose – The purpose of this paper is to present numerical investigation of the gas/vapor bubble dynamics under the influence of an ultrasonic field to give a more comprehensive understanding of the phenomenon and present new results Design/methodology/approach – In order to formulate the mathematical model, a set of governing equations for the gas inside the bubble and the liquid surrounding it are used. All hydrodynamics forces acting on the bubble are considered in the typical solution. The systems of equations required to be solved consist of ordinary and partial differential equations, w

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Pantazis, Yannis, and Ioannis Tsamardinos. "A unified approach for sparse dynamical system inference from temporal measurements." Bioinformatics 35, no. 18 (2018): 3387–96. http://dx.doi.org/10.1093/bioinformatics/btz065.

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Abstract Motivation Temporal variations in biological systems and more generally in natural sciences are typically modeled as a set of ordinary, partial or stochastic differential or difference equations. Algorithms for learning the structure and the parameters of a dynamical system are distinguished based on whether time is discrete or continuous, observations are time-series or time-course and whether the system is deterministic or stochastic, however, there is no approach able to handle the various types of dynamical systems simultaneously. Results In this paper, we present a unified approa

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Tirkey, Jeevan, Hari Gupta, and Shailendra Shukla. "Integrated gas dynamic and thermodynamic computational modeling of multicylinder 4-stroke spark ignition engine using gasoline as a fuel." Thermal Science 13, no. 3 (2009): 113–30. http://dx.doi.org/10.2298/tsci0903113t.

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This paper presents a computational tool for the evaluation of engine performance and exhaust emissions for four stroke multi-cylinder spark ignition engine which uses gasoline as a fuel. Gas dynamics flow in multi-cylinder intake and exhaust systems are modeled by using one-dimensional unsteady compressible flow equations. The hyperbolic partial differential equations are transferred into a set of ordinary differential equations by using method of characteristics and solved by finite difference method. Compatibility relationships between local fluid velocity and sonic velocity are expressed i

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Dissertations / Theses on the topic "Ordinary Differential Equations, Difference Equations and Dynamical Systems"

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Duke, Elizabeth R. "Solving higher order dynamic equations on time scales as first order systems." Huntington, WV : [Marshall University Libraries], 2006. http://www.marshall.edu/etd/descript.asp?ref=653.

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Hall, Kelli J. "Dynamic equations on changing time scales dynamics of given logistic problems, parameterization, and convergence of solutions /." Huntington, WV : [Marshall University Libraries], 2005. http://www.marshall.edu/etd/descript.asp?ref=636.

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Otunuga, Olusegun Michael. "Finding positive solutions of boundary value dynamic equations on time scale." [Huntington, WV : Marshall University Libraries], 2009. http://www.marshall.edu/etd/descript.asp?ref=997.

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Zhou, Bo. "The existence of bistable stationary solutions of random dynamical systems generated by stochastic differential equations and random difference equations." Thesis, Loughborough University, 2009. https://dspace.lboro.ac.uk/2134/14255.

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In this thesis, we study the existence of stationary solutions for two cases. One is for random difference equations. For this, we prove the existence and uniqueness of the stationary solutions in a finite-dimensional Euclidean space Rd by applying the coupling method. The other one is for semi linear stochastic evolution equations. For this case, we follows Mohammed, Zhang and Zhao [25]'s work. In an infinite-dimensional Hilbert space H, we release the Lipschitz constant restriction by using Arzela-Ascoli compactness argument. And we also weaken the globally bounded condition for F by applyin

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Kama, Phumezile. "Non-standard finite difference methods in dynamical systems." Thesis, Pretoria : [s.n.], 2009. http://upetd.up.ac.za/thesis/available/etd-07132009-163422.

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Foley, Dawn Christine. "Applications of State space realization of nonlinear input/output difference equations." Thesis, Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/16818.

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Machete, R. L. "Modelling a Moore-Spiegel Electronic Circuit : the imperfect model scenario." Thesis, University of Oxford, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.445775.

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The goal of this thesis is to investigate model imperfection in the context of forecasting. We focus on an electronic circuit built in a laboratory and then enclosed to reduce environmental effects. The non-dimensionalised model equations, obtained by applying Kirchhoff’s current and voltage laws, are the Moore-Spiegel Equations [47], but they exhibit a large disparity with the circuit. At parameter values used in the circuit, they yield a periodic trajectory whilst the circuit exhibits chaotic behaviour. Therefore, alternative models for the circuit are sought. The models we consider are loca

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Thai, Son Doan. "Lyapunov Exponents for Random Dynamical Systems." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-25314.

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In this thesis the Lyapunov exponents of random dynamical systems are presented and investigated. The main results are: 1. In the space of all unbounded linear cocycles satisfying a certain integrability condition, we construct an open set of linear cocycles have simple Lyapunov spectrum and no exponential separation. Thus, unlike the bounded case, the exponential separation property is nongeneric in the space of unbounded cocycles. 2. The multiplicative ergodic theorem is established for random difference equations as well as random differential equations with random delay. 3. We provide a co

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Hays, Joseph T. "Parametric Optimal Design Of Uncertain Dynamical Systems." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/28850.

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This research effort develops a comprehensive computational framework to support the parametric optimal design of uncertain dynamical systems. Uncertainty comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it; not accounting for uncertainty may result in poor robustness, sub-optimal performance and higher manufacturing costs. Contemporary methods for the quantification of uncertainty in dynamical system

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Dunton, Alec. "Topological Data Analysis for Systems of Coupled Oscillators." Scholarship @ Claremont, 2016. http://scholarship.claremont.edu/hmc_theses/79.

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Coupled oscillators, such as groups of fireflies or clusters of neurons, are found throughout nature and are frequently modeled in the applied mathematics literature. Earlier work by Kuramoto, Strogatz, and others has led to a deep understanding of the emergent behavior of systems of such oscillators using traditional dynamical systems methods. In this project we outline the application of techniques from topological data analysis to understanding the dynamics of systems of coupled oscillators. This includes the examination of partitions, partial synchronization, and attractors. By looking for

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Books on the topic "Ordinary Differential Equations, Difference Equations and Dynamical Systems"

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Capietto, Anna. Stability and Bifurcation Theory for Non-Autonomous Differential Equations: Cetraro, Italy 2011, Editors: Russell Johnson, Maria Patrizia Pera. Springer Berlin Heidelberg, 2013.

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Wolfgang, Kliemann, ed. Dynamical systems and linear algebra. American Mathematical Society, 2014.

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Dzhamay, Anton, Ken'ichi Maruno, and Christopher M. Ormerod. Algebraic and analytic aspects of integrable systems and painleve equations: AMS special session on algebraic and analytic aspects of integrable systems and painleve equations : January 18, 2014, Baltimore, MD. American Mathematical Society, 2015.

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Ordinary differential equations and dynamical systems. American Mathematical Society, 2011.

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Sideris, Thomas C. Ordinary Differential Equations and Dynamical Systems. Atlantis Press, 2013. http://dx.doi.org/10.2991/978-94-6239-021-8.

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1980-, Blazquez-Sanz David, Morales Ruiz, Juan J. (Juan José), 1953-, and Lombardero Jesus Rodriguez 1961-, eds. Symmetries and related topics in differential and difference equations: Jairo Charris Seminar 2009, Escuela de Matematicas, Universidad Sergio Arboleda, Bogotá, Colombia. American Mathematical Society, 2011.

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V, Anosov D., and Arnolʹd V. I. 1937-, eds. Ordinary differential equations and smooth dynamical systems. Springer-Verlag, 1988.

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V, Anosov D., ed. Ordinary differential equations and smooth dynamical systems. Springer, 1997.

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Ordinary differential equations: From calculus to dynamical systems. The Mathematical Association of America, 2014.

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Graham, Jan O'Hara. Buster Brown's alphabet safari. Buster Brown Apparel, 1995.

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Book chapters on the topic "Ordinary Differential Equations, Difference Equations and Dynamical Systems"

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Tu, Pierre N. V. "Review of Ordinary Differential Equations." In Dynamical Systems. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-78793-5_2.

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Tu, Pierre N. V. "Review of Ordinary Differential Equations." In Dynamical Systems. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-02779-0_2.

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Holzbecher, Ekkehard. "Ordinary Differential Equations: Dynamical Systems." In Environmental Modeling. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22042-5_9.

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Sparrow, Colin. "Dynamics of Ordinary Differential Equations." In Real and Complex Dynamical Systems. Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8439-5_8.

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Palmer, Ken. "Hyperbolic Sets of Ordinary Differential Equations." In Shadowing in Dynamical Systems. Springer US, 2000. http://dx.doi.org/10.1007/978-1-4757-3210-8_7.

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Chicone, Carmen. "Stability Theory of Ordinary Differential Equations." In Mathematics of Complexity and Dynamical Systems. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-1806-1_106.

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Bhatia, Nam Parshad, and George Philip Szegö. "ϱ1-Liapunov Functions for Ordinary Differential Equations." In Stability Theory of Dynamical Systems. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-62006-5_9.

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Kawan, Christoph. "Entropy of Nonautonomous Dynamical Systems." In Differential and Difference Equations with Applications. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-75647-9_15.

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Han, Xiaoying, and Peter E. Kloeden. "Random Dynamical Systems." In Random Ordinary Differential Equations and Their Numerical Solution. Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6265-0_4.

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Anguiano, María, Tomás Caraballo, José Real, and José Valero. "Pullback Attractors for NonAutonomous Dynamical Systems." In Differential and Difference Equations with Applications. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7333-6_15.

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Conference papers on the topic "Ordinary Differential Equations, Difference Equations and Dynamical Systems"

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Siami, A., and M. Farid. "Identification and Defect Detection of Continuous Dynamic Systems." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-14364.

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This paper presents a systematic and efficient algorithm using a coupled finite element - finite difference - least square method for identification and defect detection of continuous system using dynamic response of such systems. First the governing partial differential equations of motion of continuous systems such as beams are reduced to a set of ordinary differential equations in time domain using finite elements. Then finite difference method is used to convert these equations into a set of algebraic equations. This set of equations is considered as a set of equality constraints of an opt

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Ahmadian, M. T., Abdolreza Pasharavesh, and Ali Fallah. "Application of Nonlocal Theory in Dynamic Pull-In Analysis of Electrostatically Actuated Micro and Nano Beams." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48862.

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One of the most important phenomena related to electrically actuated micro and nano electromechanical systems (MEMS\NEMS) is dynamic pull-in instability which occurs when the electrical attraction and beam inertia forces are more than elastic restoring force of the beam. According to failure of classical mechanics constitutive equations in prediction of dynamic behavior of small size systems, nonlocal theory is implemented here to analyze the dynamic pull-in behavior. Equation of motion of an electrostatically actuated micro to nano scale doubly clamped beam is rewritten using differential for

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Botros, K. K., P. J. Campbell, and D. B. Mah. "Dynamic Simulation of Compressor Station Operation Including Centrifugal Compressor and Gas Turbine." In ASME 1990 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1990. http://dx.doi.org/10.1115/90-gt-344.

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Dynamic simulation of the operation of a compressor station requires mathematical modelling of the dynamic behaviour of the compressor unit and various piping elements. Such models consist of large systems of non-linear partial differential equations describing the pipe flow together with non-linear algebraic equations describing the quasi-steady flow through various valves, constrictions and compressors. In addition, the models also include mathematical descriptions of the control system which consists of mixed algebraic and ordinary differential (mad) equations with some inequalities represe

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Tirkey, J. V., H. N. Gupta, and S. K. Shukla. "Integrated Gas Dynamic and Thermodynamic Computational Modeling of Multicylinder 4-Stroke Spark Ignition Engine Using Gasoline as Fuel." In ASME 2008 Heat Transfer Summer Conference collocated with the Fluids Engineering, Energy Sustainability, and 3rd Energy Nanotechnology Conferences. ASMEDC, 2008. http://dx.doi.org/10.1115/ht2008-56497.

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This paper presents a computational tool for the evaluation of engine performance and exhaust emissions for four stroke multi-cylinder spark ignition engine which uses gasoline as fuel. Gas dynamics flow in multi-cylinder intake and exhaust systems are modeled by using one dimensional unsteady compressible flow equations. The hyperbolic partial differential equations are transferred into a set of ordinary differential equations by using method of characteristics and solved by finite difference method. Compatibility relationships between local fluid velocity (U) and sonic velocity (a) are expre

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Morini, M., M. Pinelli, and M. Venturini. "Development of a One-Dimensional Modular Dynamic Model for the Simulation of Surge in Compression Systems." In ASME Turbo Expo 2006: Power for Land, Sea, and Air. ASMEDC, 2006. http://dx.doi.org/10.1115/gt2006-90134.

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The paper deals with the development of a non-linear one-dimensional modular dynamic model for the simulation of transient behavior of compression systems. The model is based on balance equations of mass, momentum and energy, which are derived through a general approach and are written by using the finite difference method. The model also takes rotating mass dynamics into account through a lumped parameter approach. Moreover, it reproduces the behavior of the system in the presence of the surge phenomenon through steady-state performance maps, which represent the compressor operation in the in

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Szabó, Zsolt, S. C. Sinha, and Gábor Stépán. "Dynamics of Pipes Containing Pulsative Flow." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/vib-4022.

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Abstract Several mechanical models exist on elastic pipes containing fluid flow. In this paper those models are considered, where the fluid is incompressible, frictionless and its velocity relative to the pipe has the same but time-periodic magnitude along the pipe at a certain time instant. The pipe can be modelled either as a chain of articulated rigid pipes or as a continuum. The dynamic behaviour of the system strongly depends on the different kinds of boundary conditions and on the fact whether the pipe is considered to be inextensible, i.e. the cross-sectional area of the pipe is constan

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Mutou, A., S. Mizuki, Y. Komatsubara, and H. Tsujita. "Behavior of Attractors During Surge in Centrifugal Compression System." In ASME 1998 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/98-gt-301.

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A dynamical system analysis method is presented, that permits the characterization of unsteady phenomena in a centrifugal compression system. The method maps one experimental time series of data into a state space in which behaviors of the compression system should be represented, and reconstructs an attractor that geometrically characterizes a state of the compression system. The time series of data were obtained by using a high response pressure transducer and an analog to digital converter at surge condition. For the reconstruction of attractors, a noise free differentiation method in time

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Cunha, Sérgio B., and Renan M. Baptista. "Pipeline Leak Detection Using a Moderate Gain Nonlinear Observer." In 2020 13th International Pipeline Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/ipc2020-9333.

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Abstract Most pipeline control systems use some sort of autonomous leak detection system as a safety feature. Among the pipeline leak detection techniques, state observers stand out as the most sophisticated and promising technique. But its use has been inhibited as the dynamic models employed so far are large and estimating the states of nonlinear systems is not trivial. Pipeline pressure and flow dynamics have been modelled in the literature by means of different numerical solutions to a pair of first order partial differential equations that express mass and linear momentum conservation. Th

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Nipp, Kaspar, Daniel Stoffer, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Mini-symposium: Ordinary Differential Equations and Dynamical Systems." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241613.

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Steyer, Andrew, and Robert Kuether. "Connecting Functions of Nonlinear Ordinary Differential Equations." In Proposed for presentation at the SIAM Conference on Applications of Dynamical Systems held May 23-27, 2021 in Virtual. US DOE, 2021. http://dx.doi.org/10.2172/1870270.

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