메뉴 건너뛰기




Volumn 2004, Issue 3, 2004, Pages 305-321

A hybrid neural network model for the dynamics of the kuramoto-sivashinsky equation

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; FEEDBACK CONTROL; GALERKIN METHODS; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS; REYNOLDS NUMBER;

EID: 10844226380     PISSN: 1024123X     EISSN: None     Source Type: Journal    
DOI: 10.1155/S1024123X0440101X     Document Type: Article
Times cited : (6)

References (35)
  • 1
    • 0001188213 scopus 로고
    • Kuramoto-sivashinsky dynamics on the center-unstable manifold
    • D. Armbruster, J. Guckenheimer, and P. Holmes, Kuramoto-Sivashinsky dynamics on the center-unstable manifold, SIAM J. Appl. Math. 49 (1989), no. 3, 676-691.
    • (1989) SIAM J. Appl. Math. , vol.49 , Issue.3 , pp. 676-691
    • Armbruster, D.1    Guckenheimer, J.2    Holmes, P.3
  • 2
    • 0001259140 scopus 로고
    • KLTOOL: A tool to analyze spatiotemporal complexity
    • D. Armbruster, R. Heiland, and E. J. Kostelich, KLTOOL: a tool to analyze spatiotemporal complexity, Chaos 4 (1994), no. 2, 421-424.
    • (1994) Chaos , vol.4 , Issue.2 , pp. 421-424
    • Armbruster, D.1    Heiland, R.2    Kostelich, E.J.3
  • 3
    • 84957122398 scopus 로고
    • Attractors of evolution partial differential equations and estimates of their dimension
    • A. V. Babin and M. I. Vishik, Attractors of evolution partial differential equations and estimates of their dimension, Russian Math. Surveys 38 (1983), 151-213.
    • (1983) Russian Math. Surveys , vol.38 , pp. 151-213
    • Babin, A.V.1    Vishik, M.I.2
  • 4
    • 0024774330 scopus 로고
    • Neural networks and principal component analysis: Learning from examples without local minima
    • P. Baldi and K. Hornik, Neural networks and principal component analysis: learning from examples without local minima, Neural Netw. 2 (1989), no. 1, 53-58.
    • (1989) Neural Netw. , vol.2 , Issue.1 , pp. 53-58
    • Baldi, P.1    Hornik, K.2
  • 7
    • 0003241758 scopus 로고
    • Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations
    • Springer-Verlag, New York
    • P. Constantin, C. Foias, B. Nicolaenko, and R. Temam, Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations, Applied Mathematical Sciences, vol. 70, Springer-Verlag, New York, 1989.
    • (1989) Applied Mathematical Sciences , vol.70
    • Constantin, P.1    Foias, C.2    Nicolaenko, B.3    Temam, R.4
  • 8
    • 0023999086 scopus 로고
    • On the dimension of the attractors in two-dimensional turbulence
    • P. Constantin, C. Foias, and R. Temam, On the dimension of the attractors in two-dimensional turbulence, Phys. D 30 (1988), no. 3, 284-296.
    • (1988) Phys. D , vol.30 , Issue.3 , pp. 284-296
    • Constantin, P.1    Foias, C.2    Temam, R.3
  • 9
    • 0000640733 scopus 로고
    • Inertial manifolds for nonlinear evolutionary equations
    • C. Foias, G. R. Sell, and R. Temam, Inertial manifolds for nonlinear evolutionary equations, J. Differential Equations 73 (1988), no. 2, 309-353.
    • (1988) J. Differential Equations , vol.73 , Issue.2 , pp. 309-353
    • Foias, C.1    Sell, G.R.2    Temam, R.3
  • 10
    • 0013326768 scopus 로고
    • On the Hausdorff dimension of an attractorfor the two-dimensional Navier-Stokes equations
    • C. Foias and R. Temam, On the Hausdorff dimension of an attractorfor the two-dimensional Navier-Stokes equations, Phys. Lett. A 93 (1983), no. 9, 451-454.
    • (1983) Phys. Lett. A , vol.93 , Issue.9 , pp. 451-454
    • Foias, C.1    Temam, R.2
  • 12
    • 0003406531 scopus 로고
    • The University of Chicago Press, Illinois
    • H. Harman, Modern Factor Analysis, The University of Chicago Press, Illinois, 1960.
    • (1960) Modern Factor Analysis
    • Harman, H.1
  • 13
    • 0003304963 scopus 로고
    • Geometric theory of semilinear parabolic equations
    • Springer-Verlag, New York
    • D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, New York, 1981.
    • (1981) Lecture Notes in Mathematics , vol.840
    • Henry, D.1
  • 14
    • 58149421595 scopus 로고
    • Analysis of a complex of statistical variables into principal components
    • H. Hotelling, Analysis of a complex of statistical variables into principal components, J. Educ. Psychol. 24 (1933), 417-441; 498-520.
    • (1933) J. Educ. Psychol. , vol.24 , pp. 417-441
    • Hotelling, H.1
  • 15
    • 0000618153 scopus 로고
    • Order and complexity in the kuramoto-sivashinsky model of weakly turbulent interfaces
    • J. M. Hyman, B. Nicolaenko, and S. Zaleski, Order and complexity in the Kuramoto-Sivashinsky model of weakly turbulent interfaces, Phys. D 23 (1986), no. 1-3, 265-292.
    • (1986) Phys. D , vol.23 , Issue.1-3 , pp. 265-292
    • Hyman, J.M.1    Nicolaenko, B.2    Zaleski, S.3
  • 16
    • 0003946510 scopus 로고
    • Principal Component Analysis
    • Springer-Verlag, New York
    • I. T. Jolliffe, Principal Component Analysis, Springer Series in Statistics, Springer-Verlag, New York, 1986.
    • (1986) Springer Series in Statistics
    • Jolliffe, I.T.1
  • 17
    • 0025448183 scopus 로고
    • Back in the saddle again: A computer assisted study of the kuramoto-sivashinsky equation
    • I. G. Kevrekidis, B. Nicolaenko, and C. Scovel, Back in the saddle again: a computer assisted study of the Kuramoto-Sivashinsky equation, SIAM J. Appl. Math. 50 (1990), no. 3, 760-790.
    • (1990) SIAM J. Appl. Math. , vol.50 , Issue.3 , pp. 760-790
    • Kevrekidis, I.G.1    Nicolaenko, B.2    Scovel, C.3
  • 18
    • 0000907576 scopus 로고
    • Reconstructing phase space from PDE simulations
    • M. Kirby and D. Armbruster, Reconstructing phase space from PDE simulations, Z. angew. Math. Phys. 43 (1992), no. 6, 999-1022.
    • (1992) Z. Angew. Math. Phys. , vol.43 , Issue.6 , pp. 999-1022
    • Kirby, M.1    Armbruster, D.2
  • 19
    • 0026113980 scopus 로고
    • Nonlinear principal component analysis using autoassociative neural networks
    • M. A. Kramer, Nonlinear principal component analysis using autoassociative neural networks, AIChE J. 37 (1991), no. 2, 233-243.
    • (1991) AIChE J. , vol.37 , Issue.2 , pp. 233-243
    • Kramer, M.A.1
  • 20
    • 0000507179 scopus 로고
    • Persistent propagation of concentration waves in dissipative media far from thermal equilibrium
    • Y. Kuramoto and T. Tsuzuki, Persistent propagation of concentration waves in dissipative media far from thermal equilibrium, Progr. Theoret. Phys. 55 (1976), 356-369.
    • (1976) Progr. Theoret. Phys. , vol.55 , pp. 356-369
    • Kuramoto, Y.1    Tsuzuki, T.2
  • 21
    • 0000375959 scopus 로고
    • Finite-dimensionality of bounded invariant sets for navier-stokes systems and other dissipative systems
    • O. A. Ladyzhenskaya, Finite-dimensionality of bounded invariant sets for Navier-Stokes systems and other dissipative systems, J. Soviet Math. 28 (1985), 714-726.
    • (1985) J. Soviet Math. , vol.28 , pp. 714-726
    • Ladyzhenskaya, O.A.1
  • 22
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • E. N. Lorenz, Deterministic nonperiodic flow, J. Atmospheric Sci. 20 (1963), 130-141.
    • (1963) J. Atmospheric Sci. , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 23
    • 0002708045 scopus 로고
    • The structure of inhomogeneous turbulent flows
    • (A. M. Yaglom and V. I. Tatarski, eds.), Nauka, Moscow
    • J. L. Lumley, The structure of inhomogeneous turbulent flows, Atmospheric Turbulence and Radio Wave Propagation (A. M. Yaglom and V. I. Tatarski, eds.), Nauka, Moscow, 1967, pp. 166-178.
    • (1967) Atmospheric Turbulence and Radio Wave Propagation , pp. 166-178
    • Lumley, J.L.1
  • 24
    • 0005750037 scopus 로고
    • Negatively invariant sets of compact maps and an extension of a theorem of Cartwright
    • J. Mallet-Paret, Negatively invariant sets of compact maps and an extension of a theorem of Cartwright, J. Differential Equations 22 (1976), no. 2, 331-348.
    • (1976) J. Differential Equations , vol.22 , Issue.2 , pp. 331-348
    • Mallet-Paret, J.1
  • 25
    • 0003290175 scopus 로고
    • On the dimension of the compact invariant sets of certain nonlinear maps
    • Dynamical Systems and Turbulence, Warwick 1980 (Coventry, 1979/1980), Springer, Berlin
    • R. Mañé, On the dimension of the compact invariant sets of certain nonlinear maps, Dynamical Systems and Turbulence, Warwick 1980 (Coventry, 1979/1980), Lecture Notes in Math., vol. 898, Springer, Berlin, 1981, pp. 230-242.
    • (1981) Lecture Notes in Math. , vol.898 , pp. 230-242
    • Mañé, R.1
  • 26
    • 0000169232 scopus 로고
    • An algorithm for least-squares estimation of nonlinear parameters
    • D. W. Marquardt, An algorithm for least-squares estimation of nonlinear parameters, J. Soc. Indust. Appl. Math. 11 (1963), 431-441.
    • (1963) J. Soc. Indust. Appl. Math. , vol.11 , pp. 431-441
    • Marquardt, D.W.1
  • 27
    • 0027063388 scopus 로고
    • Discrete- Vs. continuous-time nonlinear signal processing of Cu electrodissolution data
    • R. Martinez, R. K. Krischer, I. G. Kevrekidis, M. Kube, and J. L. Hudson, Discrete- vs. continuous-time nonlinear signal processing of Cu electrodissolution data, Chem. Eng. Comm. 118 (1992), 25-48.
    • (1992) Chem. Eng. Comm. , vol.118 , pp. 25-48
    • Martinez, R.1    Krischer, R.K.2    Kevrekidis, I.G.3    Kube, M.4    Hudson, J.L.5
  • 28
    • 0000246863 scopus 로고
    • Turbulence and the dynamics of coherent structures. I. Coherent structures
    • L. Sirovich, Turbulence and the dynamics of coherent structures. I. Coherent structures, Quart. Appl. Math. 45 (1987), no. 3, 561-571.
    • (1987) Quart. Appl. Math. , vol.45 , Issue.3 , pp. 561-571
    • Sirovich, L.1
  • 29
    • 0031389364 scopus 로고    scopus 로고
    • Artificial neural network-based low-dimensional model for spatio-temporally varying cellular flames
    • N. Smaoui, Artificial neural network-based low-dimensional model for spatio-temporally varying cellular flames, Appl. Math. Modelling 21 (1997), 739-748.
    • (1997) Appl. Math. Modelling , vol.21 , pp. 739-748
    • Smaoui, N.1
  • 30
    • 0033731429 scopus 로고    scopus 로고
    • An artificial neural network noise reduction method for chaotic attractors
    • _, An artificial neural network noise reduction method for chaotic attractors, Int. J. Comput. Math. 73 (2000), no. 4, 417-431.
    • (2000) Int. J. Comput. Math. , vol.73 , Issue.4 , pp. 417-431
  • 31
    • 0036289618 scopus 로고    scopus 로고
    • A model for the unstable manifold of the bursting behavior in the 2D Navier-Stokes flow
    • _, A model for the unstable manifold of the bursting behavior in the 2D Navier-Stokes flow, SIAM J. Sci. Comput. 23 (2001), no. 3, 824-839.
    • (2001) SIAM J. Sci. Comput. , vol.23 , Issue.3 , pp. 824-839
  • 32
    • 3042518384 scopus 로고    scopus 로고
    • Linear versus nonlinear dimensionality reduction of high-dimensional dynamical system
    • _, Linear versus nonlinear dimensionality reduction of high-dimensional dynamical system, SIAM J. Sci. Comput. 25 (2004), no. 6, 2107-2125.
    • (2004) SIAM J. Sci. Comput. , vol.25 , Issue.6 , pp. 2107-2125
  • 33
    • 0141906256 scopus 로고    scopus 로고
    • Analyzing the dynamics of cellular flames using Karhunen-Loëve decomposition and autoassociative neural networks
    • N. Smaoui and S. Al-Yakoob, Analyzing the dynamics of cellular flames using Karhunen-Loëve decomposition and autoassociative neural networks, SIAM J. Sci. Comput. 24 (2003), no. 5, 1790-1808.
    • (2003) SIAM J. Sci. Comput. , vol.24 , Issue.5 , pp. 1790-1808
    • Smaoui, N.1    Al-Yakoob, S.2
  • 34
    • 0031215981 scopus 로고    scopus 로고
    • Symmetry and the karhunen-loève analysis
    • N. Smaoui and D. Armbruster, Symmetry and the Karhunen-Loève analysis, SIAM J. Sci. Comput. 18 (1997), no. 5, 1526-1532.
    • (1997) SIAM J. Sci. Comput. , vol.18 , Issue.5 , pp. 1526-1532
    • Smaoui, N.1    Armbruster, D.2
  • 35
    • 10844260955 scopus 로고    scopus 로고
    • Controlling the dynamics of the kuramoto-sivashinsky equation
    • N. Smaoui and M. Zribi, Controlling the dynamics of the Kuramoto-Sivashinsky equation, Int. J. Pure Appl. Math. 7 (2003), no. 3, 271-293.
    • (2003) Int. J. Pure Appl. Math. , vol.7 , Issue.3 , pp. 271-293
    • Smaoui, N.1    Zribi, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.