Chaos on the Web

Physics 161: Introduction to Chaos


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

  1. E.N. Lorenz, Deterministic Nonperiodic Flow, J. Atmos. Sc. 20, 130 (1963)
  2. R.M. May, Simple mathematical models with very complicated dynamics, Nature 261, 459 (1976)
  3. A. Wolf, J.B. Swift, H.L. Swinney and J.A. Vastano, Determining Lyapunov exponents from a time series, Physica 16D 285 (1985)
  4. K. Geist, U. Parlitz, and W. Lauterborn, Comparison of different methods for computing Lyapunov exponents, Prog. Theor. Phys. 83, 875 (1990)
  5. J.-P. Eckmann and D. Ruelle, Ergodic theory of chaos and strange attractors, Rev. Mod. Phys. 57, 617 (1985)
  6. J.D. Farmer, Information dimension and the probabilistic structure of chaos, Z. Nat. 37a, 1304 (1982)
  7. 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)
  8. J.D. Farmer, E. Ott, and J.A. Yorke, The dimension of chaotic attractors, Physica 7D 153 (1983)
  9. P. Grassberger and I. Procaccia, Estimation of the Kolmnogorov entropy from a chaotic signal, Phys. Rev. A28, 2591 (1983)
  10. G. Ahlers, Low-temperature studies of the Rayleigh-Benard instability and turbulence, Phys. Rev. Lett. 33, 1185 (1974)
  11. J.P. Gollub and H.L. Swinney, Onset of turbulence in a rotating fluid Phys. Rev. Lett. 35, 927 (1975)

Volume 2

  1. M. Dubois and P. Berge, Instabilities de couche limite dans un fluide en convection, J. de Physique 42, 167 (1981)
  2. 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)
  3. J.-C. Roux, R.H. Simoyi, and H.L. Swinney, Observation of a strange attractor, Physica 8D, 257 (1983)
  4. R.H. Simoyi, A. Wolf and H.L Swinney, One-dimensional dynamics in a multicomponent chemical reaction, Phys. Rev. Lett. 49, 245 (1982)
  5. R. Hegger, H. Kantz, and T. Schreiber, Practical implementation of nonlinear time series methods: The TISEAN package, Chaos 9, 413 (1999)
  6. 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)
  7. D.R Chialvo, R.F. Gilmour, and J. Jalife, Low dimensional chaos in cardiac tissue, Nature 343, 653 (1990)
  8. 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)
  9. Z. Qu, J.N. Weiss, and A. Garfinkel, Spatiotemporal chaos in simulated ring of cardiac tissue, Phys. Rev. Lett. 78, 1387 (1997)
  10. A. Karma, Electrical alternans and spiral wave breakup in cardiac tissue, Chaos 4, 461 (1994)
  11. M.J. Feigenbaum, Universal behavior in nonlinear systems, Los Alamos Science 1,1 (1980)
  12. J. Crutchfield, M. Nauennberg, and J. Rudnick, Scaling for external noise at the onset of chaos, Phys. Rev. Lett. 46, 933 (1981)
  13. P. Bak, T. Bohr, and M.H. Jensen, Mode-locking and the transition to chaos in dissipative systems, Physica Scripta T9, 50 (1985)
  14. J.A. Glazier and A. Libchaber, Quasiperiodicity and dynamical systems: an experimentalist's view, IEEE Trans. Circ. and Sys. 35, 790 (1988)
  15. 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)
  16. 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

  1. E. Ott, C. Grebogi, and J.A. Yorke, Controlling chaos, Phys. Rev. Lett. 64, 1196 (1990)
  2. T. Shinbrot, E.Ott, C. Grebogi, and J.A. Yorke, Using small perturbations to control chaos, Nature 363, 411 (1993)
  3. W.L. Ditto, S.N. Rauso, and M.L. Spano, Experimental control of chaos, Phys. Rev. Lett. 65, 3211 (1990)
  4. A. Garfinkel, M.L. Spano, W.L. Ditto, and J.N. Weiss, Controlling cardiac chaos, Science 257, 1230 (1992)
  5. E. Barreto and C. Grebogi, Multiparameter control of chaos, Phys. Rev. E52, 3553 (1995)
  6. T. Shinbrot, E.Ott, C. Grebogi and J.A. Yorke, Using chaos to direct trajectories to targets, Phys. Rev. Lett. 65, 3215 (1990)
  7. L.M. Pecora and T.L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett. 64, 821 (1990)
  8. 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)
  9. 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)
  10. T. Sauer, C. Grebogi, and J.A. Yorke, How long do numerical chaotic solutions remain valid?, Phys. Rev. Lett. 79, 59 (1997)
  11. R.H.G. Helleman, Self generated chaotic behavior in nonlinear mechanics, (reprinted from Fundamental Problems in Statistical Mechanics, North Holland)
  12. L.O. Chua , The Genesis of Chua's Circuit, AEU 46, 250 (1992)
  13. 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