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Volumn 80, Issue 3, 2012, Pages 192-202

Experiments with a malkus-lorenz water wheel: Chaos and synchronization

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EID: 84857469504     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.3680533     Document Type: Article
Times cited : (15)

References (41)
  • 1
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.
    • Lorenz E.N. Deterministic nonperiodic flow. J. Atmos. Sci. 1963, 20:130-141. 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 2
    • 0000737887 scopus 로고
    • The route to chaos in a dripping water faucet
    • 10.1119/1.16783
    • Dreyer K. Hickey F.R. The route to chaos in a dripping water faucet. Am. J. Phys. 1991, 59:619-627. 10.1119/1.16783.
    • (1991) Am. J. Phys. , vol.59 , pp. 619-627
    • Dreyer, K.1    Hickey, F.R.2
  • 3
    • 0001553819 scopus 로고    scopus 로고
    • Controlling chaos with simple limiters
    • 10.1103/PhysRevLett.84.3835
    • Corron N.J. Pethel S.D. Hopper B.A. Controlling chaos with simple limiters. Phys. Rev. Lett. 2000, 84:3835-3838. 10.1103/PhysRevLett.84.3835.
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 3835-3838
    • Corron, N.J.1    Pethel, S.D.2    Hopper, B.A.3
  • 4
    • 0344459334 scopus 로고
    • Experimental evidence of chaotic states in the Belousov-Zhabotinskii reaction
    • 10.1063/1.435267
    • Schmitz R.A. Graziani K.R. Hudson J.L. Experimental evidence of chaotic states in the Belousov-Zhabotinskii reaction. J. Chem. Phys. 1977, 67:3040-3044. 10.1063/1.435267.
    • (1977) J. Chem. Phys. , vol.67 , pp. 3040-3044
    • Schmitz, R.A.1    Graziani, K.R.2    Hudson, J.L.3
  • 8
    • 77949551504 scopus 로고    scopus 로고
    • Broadband chaos generated by an optoelectronic oscillator
    • 10.1103/PhysRevLett.104.113901
    • Callan K.E. Illing L. Gao Z. Gauthier D.J. Schöll E. Broadband chaos generated by an optoelectronic oscillator. Phys. Rev. Lett. 2010, 104:113901. 10.1103/PhysRevLett.104.113901.
    • (2010) Phys. Rev. Lett. , vol.104 , pp. 113901
    • Callan, K.E.1    Illing, L.2    Gao, Z.3    Gauthier, D.J.4    Schöll, E.5
  • 9
    • 0004154108 scopus 로고
    • (University of Washington Press, Seattle, WA)
    • Lorenz E.N. The Essence of Chaos 1993, (University of Washington Press, Seattle, WA)
    • (1993) The Essence of Chaos
    • Lorenz, E.N.1
  • 10
    • 0000286947 scopus 로고
    • Non-periodic convection at high and low Prandtl number
    • Malkus W.V. R. Non-periodic convection at high and low Prandtl number. Mem. Soc. R. Sci. Liege Collect. 1972, 4:125-128.
    • (1972) Mem. Soc. R. Sci. Liege Collect. , vol.4 , pp. 125-128
    • Malkus, W.V.R.1
  • 12
    • 0029276820 scopus 로고
    • Chaos in a real system
    • 10.1177/003754979506400305.
    • Tylee J.L. Chaos in a real system. Simulation 1995, 64:176-183. 10.1177/003754979506400305.
    • (1995) Simulation , vol.64 , pp. 176-183
    • Tylee, J.L.1
  • 13
  • 14
    • 0000884776 scopus 로고
    • Magnetic braking: Improved theory
    • 10.1119/1.15570.
    • Heald M.A. Magnetic braking: Improved theory. Am. J. Phys. 1988, 56:521-522. 10.1119/1.15570.
    • (1988) Am. J. Phys. , vol.56 , pp. 521-522
    • Heald, M.A.1
  • 15
    • 0000080283 scopus 로고
    • Magnetic drag in the quasi-static limit: A computational method
    • 10.1119/1.16623
    • Marcuso M. Gass R. Jones D. Rowlett C. Magnetic drag in the quasi-static limit: A computational method. Am. J. Phys. 1991, 59:1118-1123. 10.1119/1.16623.
    • (1991) Am. J. Phys. , vol.59 , pp. 1118-1123
    • Marcuso, M.1    Gass, R.2    Jones, D.3    Rowlett, C.4
  • 16
    • 84857493734 scopus 로고    scopus 로고
    • Since one can assume the air drag to be linear in the angular velocity, it is included in this analysis and contributes to κ.
    • Since one can assume the air drag to be linear in the angular velocity, it is included in this analysis and contributes to κ.
  • 17
    • 37349087524 scopus 로고    scopus 로고
    • The Malkus-Lorenz water wheel revisited
    • 10.1119/1.2785209.
    • Matson L.E. The Malkus-Lorenz water wheel revisited. Am. J. Phys. 2007, 75:1114-1122. 10.1119/1.2785209.
    • (2007) Am. J. Phys. , vol.75 , pp. 1114-1122
    • Matson, L.E.1
  • 18
    • 84857485725 scopus 로고    scopus 로고
    • We use Loc-Line hoses and nozzles.
    • We use Loc-Line hoses and nozzles.
  • 19
    • 84857463510 scopus 로고    scopus 로고
    • DigiFlow 8000T.
    • DigiFlow 8000T.
  • 22
    • 0001201892 scopus 로고    scopus 로고
    • Computer assisted proof of chaos in the Lorenz equations
    • 10.1016/S0167-2789(97)00233-9
    • Galias Z. Zgliczynski P. Computer assisted proof of chaos in the Lorenz equations. Physica D 1998, 115:165-188. 10.1016/S0167-2789(97)00233-9.
    • (1998) Physica D , vol.115 , pp. 165-188
    • Galias, Z.1    Zgliczynski, P.2
  • 23
    • 0033563546 scopus 로고    scopus 로고
    • The Lorenz attractor exists
    • 10.1016/S0764-4442(99)80439-X.
    • Tucker W. The Lorenz attractor exists. C. R. Acad. Sci. Ser. I: Math. 1999, 328:1197-1202. 10.1016/S0764-4442(99)80439-X.
    • (1999) C. R. Acad. Sci. Ser. I: Math. , vol.328 , pp. 1197-1202
    • Tucker, W.1
  • 24
    • 0035216342 scopus 로고    scopus 로고
    • Chaos in the Lorenz equations: A computer assisted proof part III: Classical parameter values
    • 10.1006/jdeq.2000.3894
    • Mischaikow K. Mrozek M. Szymczak A. Chaos in the Lorenz equations: A computer assisted proof part III: Classical parameter values. J. Diff. Eqs. 2001, 169:17-56. 10.1006/jdeq.2000.3894.
    • (2001) J. Diff. Eqs. , vol.169 , pp. 17-56
    • Mischaikow, K.1    Mrozek, M.2    Szymczak, A.3
  • 28
    • 84857474952 scopus 로고    scopus 로고
    • Chaos synchronization was independently discovered three times: by H. Fujisaka and T. Yamada in Japan [Prog. Theor. Phys. 69, 32-47 (1983)], by V. S. Afraimovich, N. N. Verichev, and M. I. Rabinovich in the USSR [Radiophys. Quantum Electron. 29, 795-803 (1986)], and by L. M. Pecora and T. L. Carroll in the US [Phys. Rev. Lett. 64, 821-824
    • Chaos synchronization was independently discovered three times: by H. Fujisaka and T. Yamada in Japan [Prog. Theor. Phys. 69, 32-47 (1983)], by V. S. Afraimovich, N. N. Verichev, and M. I. Rabinovich in the USSR [Radiophys. Quantum Electron. 29, 795-803 (1986)], and by L. M. Pecora and T. L. Carroll in the US [Phys. Rev. Lett. 64, 821-824 (1990)].
  • 29
    • 34547207039 scopus 로고    scopus 로고
    • Adaptive observer-based synchronization of the nonlinear nonpassifiable systems
    • 10.1134/S0005117907070077
    • Andrievskii B.R. Nikiforov V.O. Fradkov A.L. Adaptive observer-based synchronization of the nonlinear nonpassifiable systems. Autom. Remote Control 2007, 68:1186-1200. 10.1134/S0005117907070077.
    • (2007) Autom. Remote Control , vol.68 , pp. 1186-1200
    • Andrievskii, B.R.1    Nikiforov, V.O.2    Fradkov, A.L.3
  • 30
    • 46749095968 scopus 로고    scopus 로고
    • Estimating parameters by autosynchronization with dynamics restrictions
    • 10.1103/PhysRevE.77.066221
    • Yu D.C. Parlitz U. Estimating parameters by autosynchronization with dynamics restrictions. Phys. Rev. E 2008, 77:066221. 10.1103/PhysRevE.77.066221.
    • (2008) Phys. Rev. E , vol.77 , pp. 066221
    • Yu, D.C.1    Parlitz, U.2
  • 31
    • 70349651749 scopus 로고    scopus 로고
    • Using synchronization of chaos to identify the dynamics of unknown systems
    • 10.1063/1.3186458
    • Sorrentino F. Ott E. Using synchronization of chaos to identify the dynamics of unknown systems. Chaos 2009, 19:033108. 10.1063/1.3186458.
    • (2009) Chaos , vol.19 , pp. 033108
    • Sorrentino, F.1    Ott, E.2
  • 33
    • 0008494528 scopus 로고
    • Determining Lyapunov exponents from a time-series
    • 10.1016/0167-2789(85)90011-9
    • Wolf A. Swift J.B. Swinney H.L. Vastano J.A. Determining Lyapunov exponents from a time-series. Physica D 1985, 16:285-317. 10.1016/0167-2789(85)90011-9.
    • (1985) Physica D , vol.16 , pp. 285-317
    • Wolf, A.1    Swift, J.B.2    Swinney, H.L.3    Vastano, J.A.4
  • 34
    • 0000471425 scopus 로고
    • Comparison of different methods for computing Lyapunov exponents
    • 10.1143/PTP.83.875
    • Geist K. Parlitz U. Lauterborn W. Comparison of different methods for computing Lyapunov exponents. Prog. Theor. Phys. 1990, 83:875-893. 10.1143/PTP.83.875.
    • (1990) Prog. Theor. Phys. , vol.83 , pp. 875-893
    • Geist, K.1    Parlitz, U.2    Lauterborn, W.3
  • 35
    • 0009809703 scopus 로고
    • Studying chaotic systems using microcomputer simulations and Lyapunov exponents
    • 10.1119/1.16163
    • Souza-Machado S.D. Rollins R.W. Jacobs D.T. Hartman J.L. Studying chaotic systems using microcomputer simulations and Lyapunov exponents. Am. J. Phys. 1990, 58:321-329. 10.1119/1.16163.
    • (1990) Am. J. Phys. , vol.58 , pp. 321-329
    • Souza-Machado, S.D.1    Rollins, R.W.2    Jacobs, D.T.3    Hartman, J.L.4
  • 36
    • 0000543733 scopus 로고
    • A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems
    • Oseledets V.I. A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems. Trans. Moscow Math. Soc. 1968, 19:197-231.
    • (1968) Trans. Moscow Math. Soc. , vol.19 , pp. 197-231
    • Oseledets, V.I.1
  • 37
    • 48749145669 scopus 로고
    • The Dimension of chaotic attractors
    • 10.1016/0167-2789(83)90125-2
    • Farmer J.D. Ott E. Yorke J.A. The Dimension of chaotic attractors. Physica D 1983, 7:153-180. 10.1016/0167-2789(83)90125-2.
    • (1983) Physica D , vol.7 , pp. 153-180
    • Farmer, J.D.1    Ott, E.2    Yorke, J.A.3
  • 38
    • 0018989294 scopus 로고
    • Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; A method for computing all of them, Part 1: Theory
    • 10.1007/BF02128236
    • Benettin G. Galgani L. Giorgilli A. Strelcyn J.M. Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; A method for computing all of them, Part 1: Theory. Meccanica 1980, 9:9-20. 10.1007/BF02128236.
    • (1980) Meccanica , vol.9 , pp. 9-20
    • Benettin, G.1    Galgani, L.2    Giorgilli, A.3    Strelcyn, J.M.4
  • 39
    • 0018992908 scopus 로고
    • Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; A method for computing all of them, Part 2: Numerical Application
    • 10.1007/BF02128237
    • Benettin G. Galgani L. Giorgilli A. Strelcyn J.M. Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; A method for computing all of them, Part 2: Numerical Application. Meccanica 1980, 9:21-30. 10.1007/BF02128237.
    • (1980) Meccanica , vol.9 , pp. 21-30
    • Benettin, G.1    Galgani, L.2    Giorgilli, A.3    Strelcyn, J.M.4
  • 41
    • 0035911773 scopus 로고    scopus 로고
    • Bounds for trajectories of the Lorenz equations: An illustration of how to choose Liapunov functions
    • 10.1016/S0375-9601(01)00109-8.
    • Swinnerton-Dyer P. Bounds for trajectories of the Lorenz equations: An illustration of how to choose Liapunov functions. Phys. Lett. A 2001, 281:161-167. 10.1016/S0375-9601(01)00109-8.
    • (2001) Phys. Lett. A , vol.281 , pp. 161-167
    • Swinnerton-Dyer, P.1


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