Közönséges differenciálegyenletek a BME Matematika Intézetéből  részletek

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Projekt adatai

  
azonosító
37491
típus K
Vezető kutató Garay Barnabás
magyar cím Közönséges differenciálegyenletek a BME Matematika Intézetéből
Angol cím Ordinary differential equations from the Mathematical Institute of the BUTE
zsűri Matematika–Számítástudomány
Kutatóhely Differenciálegyenletek Tanszék (Budapesti Műszaki és Gazdaságtudományi Egyetem)
résztvevők Bozi Imre
Gyurkovics Éva
Halmschlager Andrea
Horváth Miklós
Lóczi Lajos
Moson Péter
Rózsa Zoltán Márk
Tóth János
projekt kezdete 2002-01-01
projekt vége 2006-12-31
aktuális összeg (MFt) 8.720
FTE (kutatóév egyenérték) 0.00
állapot lezárult projekt





 

Zárójelentés

  
kutatási eredmények (magyarul)
A kutatási feladat két fő célja az volt, hogy eredményeket érjünk el (1) a végtelen dimenziós dinamika, valamint a (2) numerika, pontosabban differenciálegyenletek numerikus analízise területén. (1) Az első céllal kapcsolatos reprezentatív eredmény HORVÁTH MIKLÓS ''Inverse spectral problems and closed exponential systems, Annals of Mathematics 162(2005), 885-918'' dolgozata, amely -- csakúgy mint a kísérő Transactions és Proceedings of the AMS cikkek -- akkor és csak akkor feltételeket ad bizonyos típusú Schrödinger operatorok potenciáljának unicitására. (2) A második céllal kapcsolatos fő eredmény -- közreműködők BÁNHELYI BALÁZS és CSENDES TIBOR (Informatika Intézet, Szeged) -- az az észrevétel, hogy az intervallum aritmetikával támogatott globális optimalizációk elmélete kényelmes keretet biztosít dinamikai rendszerek kaotikus voltának számítógép által segített bizonyítására. Az elméleti újdonság az, hogy az algebrai topógia eszköztára, jelesen a korábbi megközelítésekre annyira jellemző Conley index és a további indexek, legalábbis az esetek egy részében, kiválthatóak a Brouwer-féle fixponttétel alkalmazásával.
kutatási eredmények (angolul)
The two main goals of the research project have been (1) results in infinite-dimensional dynamics, and (2) results in numerics--more precisely, in the numerics of differential equations. (1) As for the first goal, the representative publication is ''Inverse spectral problems and closed exponential systems, Annals of Mathematics 162(2005), 885-918'' by MIKLÓS HORVÁTH. Together with the accompanying papers in the Transaction and the Proceedings of the AMS, the ''Inverse spectral problems and closed exponential systems'' establishes if and only if conditions on the uniqueness of the potential of certain Schrödinger operators. (2) As for the second goal, the main result--achieved in cooperation with BALÁZS BÁNHELYI and TIBOR CSENDES, Szeged Institute of Informatics--is that interval arithmetics based global optimization constitutes a comfortable framework for computer-assisted proofs of chaotic behaviour of dynamical systems. The theoretical novelty is that tools from algebraic topology including Conley and other indices in earlier approaches can be, at least in several cases, replaced by applications of the Brouwer fixed point theorem.
a zárójelentés teljes szövege http://real.mtak.hu/227/
döntés eredménye
igen





 

Közleményjegyzék

  
Halmschlager A; Matolcsi T: Minimal positive realizations for a class of transfer functions, IEEE Transactions Circuit Systems Fundamental Theory Applications 52: 177-180, 2004
Elbert A; Garay BM: Differential equations: Hungary, the extended first half of the 20th century, A panorama of Hungarian mathematics in the Twentieth Century I. (Ed J.Horvath), Springer, Berlin , pp. 245-294, 2005
Garay BM; Garay J: Total separation and asymptotic stability, Univ Acta Iagel Acta Math 40: 125-136, 2002
Garay BM; Hofbauer J: Robust permanence for ecological differential equations, minimax, and discretization, SIAM J Math Anal 34: 1007-1039, 2003
Garay BM; Loczi L: Monoton delay equations and Runge-Kutta discretization, Funct Differ Equ 11: 59-67, 2004
Garay BM; Hilger S; Kloeden PE: Continuous dependence in time scale dynamics, Proc. Conf. Difference Equations (Augsburg 2002) CRC Press, Boca Raton, pp. 279-287, 2004
Gyurkovics E, Takacs T: Quadratic stabilization with H-infinity norm bound on nonlinear discrete-time uncertain systems with bounded control, Systems Control Lett 50: 277-289, 2003
Loczi L: The gradient-Fourier method for nonlinear Neumann boundary value problems and its algorithmic realization in Mathematica, Pure Math Appl 13: 211-225, 2002
Horvath M: On the first two eigenvalues of Sturm-Liouville operators, Proc Amer Math Soc 131: 1215-1224, 2003
Gaveau B; Martinas K; Moreau M; Toth J: Entropy, extropy and information potential in stochastioc systems far from equilibrium, Phys A 305: 445-466, 2002
Schuman B; Toth J: No limit cycle in two species second order kinetics, Bull Sci Math 127: 222-230, 2003
Gyurkovics E; Elaiw AM: Stabilization of sampled-data nonlinear systems by receding horizon via discrete-time approximation, Automatica 40: 2017-2028, 2004
Halmschlager A; Szenthe L; Toth J: Invariants of kinetic differential equations, Electronic J Qualitative Theory Differ Eq 14: 1-14, 2004
Kovacs K; Vizvari B; Riedel M; Toth J: Decomposition of the permanganate/oxalic acid overall reaction to elementary steps based on integer programming theory, Phys Chem Chem Phys 6: 1236-1242, 2004
Rozsa Z; Toth J: Exact linear lumping in abstract spaces, Electronic J Qualitative Theory Differ Eq 21: 1-20, 2004
Halmschlager A; Toth J:: Über Theorie und Anwendung von polynominalen Differentialgleichungen, Wissenschaftliche Mitteilungen der 16. Frühlungsakademie, München, pp. 35-40, 2004
Ladics T: The analysis of the splitting error for advection-reaction problems in air pollution models, Időjárás 109: 173-188, 2004
Papp D; Vízvári B: Effective solution of linear Diophantine equation systems with an application in chemistry, J Mathematical Chemistry (in print), 2006
Halmschlager A; Tandori J; Trotta M; Rinyu L; Pfeiffer I; Nagy L: A mathematical model for quinone-herbicide competition in the reaction-centres of 'Rhodobacter sphareoides', Funct. Plant Biology 29: 443-449, 2002
Gyurkovics E; Svirko D: A tracking controller for flexible joint robots based on separation principle, Hungarian Electronic J. Sci., Appl. Num.. Math. Ser. No. ANM-020805-A, pp. 11, 2002
Gyurkovics E; Svirko D: A tracking controller for flexible joint robots, J. Electrical Engineering 53: 187-190, 2002
Gyurkovics E; Svirko D: A nonlinear observer for flexible joint robots, Periodica Polytechnica Ser. Mech. Eng. 46: 127-137, 2002
Gyurkovics E; Takacs T: Guaranteeing cost strategies for infinite horizon difference games with uncertain dynamics, Internat. J. Control 78: 587-599, 2005
Gyurkovics E; Elaiw A: A stabilizing sampled-data 1-step receding control with application to a HIV/AIDS model, Differential Equations and Dynamical Systems (in print), 2006
Horvath M; Kiss M: A bound for ratios of eigenvalues of Schrödinger operators with single-well potential, Proc Amer Math Soc (in print), 2006
Gyurkovics E; Meyer D; Takacs T: Budget balancing in a two-dimensional macroeconomic model, Mathematical Modelling of Dynamical Systems (in print), 2006
Tóth J; Simon PL: Differenciálegyenletek. Bevezetés az elméletbe és az alkalmazásokba, Typotex, Budapest, 2005
Horvath M; Kiss M: A bound for ratios of eigenvalues of Schrödinger operators on the real line, Discrete Continuous Dynamical Systems 13 Supplement: 403-409, 2005
Gyurkovics E; Elaiw A: Stabilizing receding horizon control of sampled-data nonlinear systems via their approximate discrete-time models, Proc. Control Applications Optimization, Visegrád, pp. 39-45, 2003
Gyurkovics E; Svirko D: A tracking controller for flexible joint robots, Proc. 11th Internat Workshop RAAD, Balatonfüred (electronic), 2002
Horvath M: Inverse spectral problems and closed exponential systems, Annals of Mathematics 162: 885-918, 2005
Horvath M: Inverse scattering with fixed energy and an inverse eigenvalue problem on the half-line, Trans Amer Math Soc (in print), 2006
Gyurkovics E; Elaiw A: Stabilization of sampled-data nonlinear systems by receding horizon via discret-time approximation, Proc. 2nd IFAC Conf. Control Systems Design, Bratislava (electronic), 2003
Gyurkovics E; Takacs T: Guaranteeing cost strategies for uncertain difference games, Proc. MNTS 2004 Mathematical Theory Networks Systems, Belgium (electronic), 2004
Gyurkovics E; Elaiw A: Stabilization of HIV/AIDS model using an 1-step receding horizon control based treatment scheduling, Proc. Symp. Nonlinear Control Systems, Stuttgart, IFAC, pp. 801-806, 2004
Gyurkovics E; Elaiw A: Multirate sampling and delays in receding horizon stabilization of nonlinear systems, Proc 16th IFAC World Congress, Prague (electronic), 2005
Karatson J; Loczi L: Sobolev gradient preconditioning for the electrostatic potential equation, Computers and Mathematics with Applications 50: 1093-1104, 2005
Gyurkovics E; Elaiw A: Conditions for MPC based stabilization of sampled-data nonlinear systems via discrete-time approximations, Proc. Internat. Workshop on Assesment and Future Directions of Nonlinear Model Predictive Control, IST, Freudenstadt-Lauterbad, pp. 97-110, 2005
Brochot C; Toth J; Bois F: Lumping in pharmacokinetics, J Pharmacokinetics and Pharmacodynamics 32: 719-736, 2005
Toth J; Rospars JP: Dynamic modelling of biochemical reactions with applications to signal transduction: Principles and tools using 'Mathematica', Biosystems 79: 33-52, 2005
Erdi P; Toth J: Towards a dynamic neuropharmacology: Integrating network and receptor levels, Brain, Vision, and Artificial Intelligence (Eds. M.DeGregorio, V.DiMaio, M.Frucci, C.Musio), LN in Computer Science 374, pp. 1-17, 2005
Gaveau B; Moreau M; Toth J: Master equations and path-integral formulation of variational principles for reactions, Variational and Extremum Principles in Macroscopic Systems (Eds. S.Sieneutycz, H.Farkas), Elsevier, pp. 315-340, 2004
Garay BM: A functional equation characterizing monomial functions used in permanence theory for ecological differential equations, Univ Acta Iagel Acta Math 42: 69-76, 2004
Erdi P; Kiss T; Toth J; Zalanyi L: From system biology to dynamical neuropharmacology, IEEE Proc. Systems Biology (submitted), 2006
Garay BM; Lee KH: Attractors and invariant manifolds under discretization with variable stepsize, Discrete Continuous Dynamical Systems 13: 827-841, 2005
Garay BM: A brief survey of numerical dynamics of functional differential equations -- Gyula Farkas (1972-2002) in memoriam, Internat J Bifurcations Chaos 15: 729-742, 2005
Banhelyi B; Csendes T; Garay BM: A verified optimization technique to locate chaotic regions of a Henon system, J Global Optimization (in print), 2006
Banhelyi B; Csendes T; Garay BM: Optimization and the Miranda approach in detecting horseshoe-type chaos by computer, Internat J Bifurcations Chaos (submitted), 2006
Fontes FACC; Gyurkovics E; Magni L: Sampled-data model predictive control for nonlinear time-varying systems: Stability and robustness, Assesment and Future Directions of Nonlinear Model Predictive Control, Eds. F.Allgöver, L.Bregler, R.Findeisen, LN Control and Information Sciences, Springer (in print), 2006
Fontes FACC; Gyurkovics E; Magni L: Sampled-data model predictive control for nonlinear time-varying systems: Stability and robustness, Proc. Internat Workshop on Assesment and Future Directions of Nonlinear Model Predictive Control, IST, Freudenstadt-Lauterbad, pp. 243-254, 2005
Gyurkovics E; Elaiw A: Conditions for MPC based stabilization of sampled-data nonlinear systems via discrete-time approximations, Assesment and Future Directions of Nonlinear Model Predictive Control, Eds. F.Allgover, L. Bregler, R.Findeisen, LN Control and Information Sciences, Springer (in print), 2006
Garay BM; Simon PL: Bifurcation analysis of an oscillatory CNN model with two cells, Stability Dynamical Systems (submitted), 2006



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