메뉴 건너뛰기




Volumn 17, Issue 4, 2007, Pages 1199-1219

Attractor modeling and empirical nonlinear model reduction of dissipative dynamical systems

Author keywords

Attractor; ISOMAP; KL analysis; Model reduction; POD; Singular perturbation

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; DATA STRUCTURES; DYNAMIC MODELS; GALERKIN METHODS; IMAGE RECOGNITION; LEARNING SYSTEMS;

EID: 34250210796     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021812740701777X     Document Type: Article
Times cited : (21)

References (61)
  • 1
    • 12044249591 scopus 로고
    • The analysis of observed chaotic data in physical systems
    • Abarbariel, H., Brown, R., Sirowich, J. & Tsimring, L. [1993] "The analysis of observed chaotic data in physical systems," Rev. Mod. Phys. 65, 1331-1392.
    • (1993) Rev. Mod. Phys , vol.65 , pp. 1331-1392
    • Abarbariel, H.1    Brown, R.2    Sirowich, J.3    Tsimring, L.4
  • 3
    • 0038455092 scopus 로고    scopus 로고
    • Graph approximations to geodesics in embedded manifolds
    • Technical report, Stanford and Carnegie Mellon
    • Bernstein, M., de Silva, V., Langford, J. C. & Tenenbaum, J. B. [2000] "Graph approximations to geodesics in embedded manifolds," Technical report, Stanford and Carnegie Mellon.
    • (2000)
    • Bernstein, M.1    de Silva, V.2    Langford, J.C.3    Tenenbaum, J.B.4
  • 4
    • 0001881608 scopus 로고
    • Knotted periodic orbits in dynamical systems-I: Lorenz's equations
    • Birman, J. & Williams, R. F. [1983] "Knotted periodic orbits in dynamical systems-I: Lorenz's equations," Topology 22, 47-82.
    • (1983) Topology , vol.22 , pp. 47-82
    • Birman, J.1    Williams, R.F.2
  • 11
    • 84982523212 scopus 로고
    • A zoo of strange attractors from the canonical Chua's circuits
    • Chua, L. O. [1992] "A zoo of strange attractors from the canonical Chua's circuits," Proc. 35th Midwest Symp. Circuits and Systems, Vol. 2, pp. 916-926.
    • (1992) Proc. 35th Midwest Symp. Circuits and Systems , vol.2 , pp. 916-926
    • Chua, L.O.1
  • 14
    • 34250212373 scopus 로고    scopus 로고
    • Cvitanovic, P. A, Dahlqvist, P, Mainieri, R, Tanner, G, Vattay, G, Whelan, N. & Wirzba, A, 2003] Classical and Quantum Chaos, Part I: Deterministic Chaos, unpublished web book, version 10.1.6
    • Cvitanovic, P. A., Dahlqvist, P., Mainieri, R., Tanner, G., Vattay, G., Whelan, N. & Wirzba, A. [2003] Classical and Quantum Chaos, Part I: Deterministic Chaos, unpublished web book, www.nbi.dk/Chaosbook, version 10.1.6.
  • 16
    • 35949018382 scopus 로고
    • Ergodic theory of chaos and strange attractors
    • Eckmann, J.-P. & Ruelle, D. [1985] "Ergodic theory of chaos and strange attractors," Rev. Mod. Phys. 57, 617-619.
    • (1985) Rev. Mod. Phys , vol.57 , pp. 617-619
    • Eckmann, J.-P.1    Ruelle, D.2
  • 18
    • 34249982739 scopus 로고
    • Predicting chaotic time series
    • Farmer, J. & Sirowich, J. [1987] "Predicting chaotic time series," Phys. Rev. Lett. 59, 845.
    • (1987) Phys. Rev. Lett , vol.59 , pp. 845
    • Farmer, J.1    Sirowich, J.2
  • 19
    • 34250627892 scopus 로고
    • Geometric singular perturbation theory for ordinary differential equations
    • Fenichel, N. [1979] "Geometric singular perturbation theory for ordinary differential equations," J. Diff. Eqs. 31, 53-98.
    • (1979) J. Diff. Eqs , vol.31 , pp. 53-98
    • Fenichel, N.1
  • 20
    • 0001047390 scopus 로고
    • Inertial manifolds for the Kuramato-Sivasinsky equation and an estimate of their lowest dimension
    • Foias, C., Nicolaenko, B., Sell, G. R. & Teman, R. [1988] "Inertial manifolds for the Kuramato-Sivasinsky equation and an estimate of their lowest dimension," J. Math. Pures. Appl. 67, 197-226.
    • (1988) J. Math. Pures. Appl , vol.67 , pp. 197-226
    • Foias, C.1    Nicolaenko, B.2    Sell, G.R.3    Teman, R.4
  • 21
    • 34548696055 scopus 로고
    • Independent coordinates for strange attractors from mutual information
    • Fraser, A. M. & Swinney, H. L. [1986] "Independent coordinates for strange attractors from mutual information," Phys. Rev. A 33, 11-34.
    • (1986) Phys. Rev. A , vol.33 , pp. 11-34
    • Fraser, A.M.1    Swinney, H.L.2
  • 26
    • 34047228827 scopus 로고
    • Approximate inertial manifolds for the Kuramato-Sivashinsky equation: Analysis and computations
    • Jolly, M. S., Kevrekidis, I. G. & Titi, E. S. [1990] "Approximate inertial manifolds for the Kuramato-Sivashinsky equation: Analysis and computations," Physica D 44, 38-60.
    • (1990) Physica D , vol.44 , pp. 38-60
    • Jolly, M.S.1    Kevrekidis, I.G.2    Titi, E.S.3
  • 27
    • 0035683176 scopus 로고    scopus 로고
    • Accurate computations on inertial manifolds
    • Jolly, M. S., Rosa, R. & Temam, R. [2001] "Accurate computations on inertial manifolds," SIAM J. Sci. Comput. 22, 2216-2238.
    • (2001) SIAM J. Sci. Comput , vol.22 , pp. 2216-2238
    • Jolly, M.S.1    Rosa, R.2    Temam, R.3
  • 28
    • 0034215357 scopus 로고    scopus 로고
    • Synchronization of chaotic systems and invariant manifolds
    • Josic, K. [2000] "Synchronization of chaotic systems and invariant manifolds," Nonlinearity 13, 1321-1336.
    • (2000) Nonlinearity , vol.13 , pp. 1321-1336
    • Josic, K.1
  • 31
    • 35949006791 scopus 로고
    • Determining embedding dimension for phase-space reconstruction using a geometrical construction
    • Kennel, M. B., Brown, R. & Abarbanel, H. D. I. [1992] "Determining embedding dimension for phase-space reconstruction using a geometrical construction," Phys. Rev. A 45, 3403.
    • (1992) Phys. Rev. A , vol.45 , pp. 3403
    • Kennel, M.B.1    Brown, R.2    Abarbanel, H.D.I.3
  • 34
    • 0000507179 scopus 로고
    • Persistent propagation of concentration waves in dissipative media far from equilibrium
    • Kuramoto & Tsuzuki, Y. T. [1976] "Persistent propagation of concentration waves in dissipative media far from equilibrium," Prof. Theor. Phys. 55, 365-369.
    • (1976) Prof. Theor. Phys , vol.55 , pp. 365-369
    • Kuramoto1    Tsuzuki, Y.T.2
  • 37
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flows
    • Lorenz, E. N. [1963] "Deterministic nonperiodic flows," J. Atmosph. Sci. 20, 130-141.
    • (1963) J. Atmosph. Sci , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 39
    • 34250195989 scopus 로고    scopus 로고
    • Matlab [2005] The Spline Toolbox, The MathWorks 7.0.4.352 (R14).
    • Matlab [2005] The Spline Toolbox, The MathWorks 7.0.4.352 (R14).
  • 40
    • 0021710645 scopus 로고    scopus 로고
    • Matsumoto, T. [1984] A chaotic attractor from Chua's circuit, IEEE Trans. Circuits Syst. CAS-31, 10551058.
    • Matsumoto, T. [1984] "A chaotic attractor from Chua's circuit," IEEE Trans. Circuits Syst. CAS-31, 10551058.
  • 41
    • 0000971706 scopus 로고
    • A comparison of a spline estimate to its equivalent kernel estimate
    • Messer, K. [1991] "A comparison of a spline estimate to its equivalent kernel estimate," Ann. Statist. 19, 817-829.
    • (1991) Ann. Statist , vol.19 , pp. 817-829
    • Messer, K.1
  • 42
    • 21844509828 scopus 로고
    • Splines as local smoothers
    • Nyschka, D. [1995] "Splines as local smoothers," Ann. Statist. 23, 1175-1197.
    • (1995) Ann. Statist , vol.23 , pp. 1175-1197
    • Nyschka, D.1
  • 46
    • 0034346757 scopus 로고    scopus 로고
    • Slow manifolds of some chaotic systems with applications to laser systems
    • Ramdani, S., Rossetto, B., Chua, L. O. & Lozi, R. [2000] "Slow manifolds of some chaotic systems with applications to laser systems," Int. J. Bifurcation and Chaos 10, 2729-2744.
    • (2000) Int. J. Bifurcation and Chaos , vol.10 , pp. 2729-2744
    • Ramdani, S.1    Rossetto, B.2    Chua, L.O.3    Lozi, R.4
  • 48
    • 0034704222 scopus 로고    scopus 로고
    • Nonlinear dimensionality reduction by locally linear embedding
    • Roweis, S. T. & Saul, L. K. [2000] "Nonlinear dimensionality reduction by locally linear embedding," Science 260, 2323 2326.
    • (2000) Science , vol.260 , pp. 2323-2326
    • Roweis, S.T.1    Saul, L.K.2
  • 49
    • 21144449758 scopus 로고    scopus 로고
    • Model reduction for fluids, using balanced proper orthogonal decomposition
    • Rowley, C. W. [2005] "Model reduction for fluids, using balanced proper orthogonal decomposition," Int. J. Bifurcation and Chaos 15, 997-1013.
    • (2005) Int. J. Bifurcation and Chaos , vol.15 , pp. 997-1013
    • Rowley, C.W.1
  • 52
    • 0024703130 scopus 로고
    • Chaotic dynamics of coherent structures
    • Sirovich, L. [1989] "Chaotic dynamics of coherent structures," Physica D 37, 126-145.
    • (1989) Physica D , vol.37 , pp. 126-145
    • Sirovich, L.1
  • 53
    • 0000779360 scopus 로고
    • Dynamical Systems and Turbulence
    • eds. Rand, D. & Young, L.-S, Springer, Berlin, p
    • Takens, F. [1980] Dynamical Systems and Turbulence, eds. Rand, D. & Young, L.-S., Lecture Notes in Mathematics, Vol. 898 (Springer, Berlin), p. 366.
    • (1980) Lecture Notes in Mathematics , vol.898 , pp. 366
    • Takens, F.1
  • 55
    • 0034704229 scopus 로고    scopus 로고
    • A global geometric framework for nonlinear dimensionality reduction
    • Tenenbaum, J. B., de Silva, V. & Langford, J. C. [2000] "A global geometric framework for nonlinear dimensionality reduction," Science 260, 2319-2323.
    • (2000) Science , vol.260 , pp. 2319-2323
    • Tenenbaum, J.B.1    de Silva, V.2    Langford, J.C.3
  • 57
    • 17044414484 scopus 로고    scopus 로고
    • A. gallery of attractors from smooth Chua's equation
    • Tsuneda, A. [2005] "A. gallery of attractors from smooth Chua's equation," Int. J. Bifurcation and Chaos 15, 1-40.
    • (2005) Int. J. Bifurcation and Chaos , vol.15 , pp. 1-40
    • Tsuneda, A.1
  • 61
    • 26344450284 scopus 로고    scopus 로고
    • Karhunen-Loeve decomposition of extensive chaos
    • Zoldi, S. M. & Greenside, H. S. [1997] "Karhunen-Loeve decomposition of extensive chaos," Phys. Rev. Lett. 78, 1687-1690.
    • (1997) Phys. Rev. Lett , vol.78 , pp. 1687-1690
    • Zoldi, S.M.1    Greenside, H.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.