Chaos on the Web
Physics 161: Introduction to Chaos
Reprints
The folders on reserve in the Millikan Library contain a number of reprints of original papers and reviews that form a useful complement to notes and textbooks.
Volume 1
- E.N. Lorenz, Deterministic Nonperiodic Flow, J. Atmos. Sc. 20, 130 (1963)
- R.M. May, Simple mathematical models with very complicated dynamics, Nature 261, 459 (1976)
- A. Wolf, J.B. Swift, H.L. Swinney and J.A. Vastano, Determining Lyapunov exponents from a time series, Physica 16D 285 (1985)
- K. Geist, U. Parlitz, and W. Lauterborn, Comparison of different methods for computing Lyapunov exponents, Prog. Theor. Phys. 83, 875 (1990)
- J.-P. Eckmann and D. Ruelle, Ergodic theory of chaos and strange attractors, Rev. Mod. Phys. 57, 617 (1985)
- J.D. Farmer, Information dimension and the probabilistic structure of chaos, Z. Nat. 37a, 1304 (1982)
- T.C. Halsey, M.H. Jensen, L.P. Kadanoff, I. Procaccia, and B.I.Shraiman, Fractal measures and their singularities: the characterization of strange sets Phys. Rev. A33, 1141 (1986)
- J.D. Farmer, E. Ott, and J.A. Yorke, The dimension of chaotic attractors, Physica 7D 153 (1983)
- P. Grassberger and I. Procaccia, Estimation of the Kolmnogorov entropy from a chaotic signal, Phys. Rev. A28, 2591 (1983)
- G. Ahlers, Low-temperature studies of the Rayleigh-Benard instability and turbulence, Phys. Rev. Lett. 33, 1185 (1974)
- J.P. Gollub and H.L. Swinney, Onset of turbulence in a rotating fluid Phys. Rev. Lett. 35, 927 (1975)
Volume 2
- M. Dubois and P. Berge, Instabilities de couche limite dans un fluide en convection, J. de Physique 42, 167 (1981)
- B. Malraison, P. Atten, P. Berge, and M. Dubois, Dimension of strange attractors: an experimental determination for the chaotic regime of two convective systems, J. de
Physique Lett.44, L897 (1983)
- J.-C. Roux, R.H. Simoyi, and H.L. Swinney, Observation of a strange attractor, Physica
8D, 257 (1983)
- R.H. Simoyi, A. Wolf and H.L Swinney, One-dimensional dynamics in a multicomponent chemical reaction, Phys. Rev. Lett.
49, 245 (1982)
- R. Hegger, H. Kantz, and T. Schreiber, Practical implementation of nonlinear time series methods: The TISEAN package, Chaos 9, 413 (1999)
- H.S. Greenside, M.C. Cross and W.M. Coughran, Mean flows and the onset of chaos in large-cell convection, Phys. Rev. Lett. 60, 2269 (1988)
- D.R Chialvo, R.F. Gilmour, and J. Jalife, Low dimensional chaos in cardiac tissue, Nature 343, 653 (1990)
- M. Watanabe, N.F. Otani, and R.F. Gilmour, Biphasic restitution of action potential duration and complex dynamics in ventricular myocardium, Circ. Res.
76, 915 (1995)
- Z. Qu, J.N. Weiss, and A. Garfinkel, Spatiotemporal chaos in simulated ring of cardiac tissue, Phys. Rev. Lett. 78, 1387 (1997)
- A. Karma, Electrical alternans and spiral wave breakup in cardiac tissue, Chaos 4, 461 (1994)
- M.J. Feigenbaum, Universal behavior in nonlinear systems, Los Alamos Science 1,1 (1980)
- J. Crutchfield, M. Nauennberg, and J. Rudnick, Scaling for external noise at the onset of chaos, Phys. Rev. Lett. 46, 933 (1981)
- P. Bak, T. Bohr, and M.H. Jensen, Mode-locking and the transition to chaos in dissipative systems, Physica Scripta T9, 50 (1985)
- J.A. Glazier and A. Libchaber, Quasiperiodicity and dynamical systems: an experimentalist's view, IEEE Trans. Circ. and Sys. 35, 790 (1988)
- J.A. Glazier, M.H. Jensen, A. Libchaber, and J. Stavans, Structure of Arnold Tongues and the f(alpha) spectrum for period doubling: experimental results
Phys. Rev. A34, 1621 (1986)
- J.A. Glazier, L.P. Kadanoff, A. Libchaber, I. Procaccia and
J. Stavans, Global universality at the onset of chaos: Results of a forced Rayleigh-Benard experiment, Phys. Rev. Lett. 55, 2798 (1985)
Volume 3
- E. Ott, C. Grebogi, and J.A. Yorke, Controlling chaos, Phys. Rev. Lett. 64, 1196 (1990)
- T. Shinbrot, E.Ott, C. Grebogi, and J.A. Yorke, Using small perturbations to control chaos, Nature 363, 411 (1993)
- W.L. Ditto, S.N. Rauso, and M.L. Spano, Experimental control of chaos, Phys. Rev. Lett. 65, 3211 (1990)
- A. Garfinkel, M.L. Spano, W.L. Ditto, and J.N. Weiss, Controlling cardiac chaos, Science 257, 1230 (1992)
- E. Barreto and C. Grebogi, Multiparameter control of chaos, Phys. Rev. E52, 3553 (1995)
- T. Shinbrot, E.Ott, C. Grebogi and J.A. Yorke, Using chaos to direct trajectories to targets, Phys. Rev. Lett. 65, 3215 (1990)
- L.M. Pecora and T.L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett. 64, 821 (1990)
- H.D.I. Arbarbanel, , T.A. Carroll, L.M. Pecora, J.D. Sidorwcih and L.S. Tsimring, Predicting physical variables in time-delay embedding, Phys. Rev. E49, 1840 (1994)
- C. Grebogi, S.M. Hammel, J.A. Yorke, and T. Sauer, Shadowing of physical trajectories in chaotic dynamics: containment and refinement, Phys. Rev. Lett. 65, 1527 (1990)
- T. Sauer, C. Grebogi, and J.A. Yorke, How long do numerical chaotic solutions remain valid?, Phys. Rev. Lett. 79, 59 (1997)
- R.H.G. Helleman, Self generated chaotic behavior in nonlinear mechanics, (reprinted from Fundamental Problems in Statistical Mechanics, North Holland)
- L.O. Chua , The Genesis of Chua's Circuit, AEU 46, 250 (1992)
- K. Murali and M. Lakshmanan, Observation of many bifurcation sequences in a driven piecewise-linear circuit, Phys. Lett. 151, 412 (1990)
Last modified Monday, January 24, 2000
Michael Cross