Bibliography for the Lorenz Attractor

unabridged

 

  1. Symbolic dynamics and periodic orbits of the Lorenz attractor
    Viswanath, D.
    Nonlinearity, 2003, vol. 16, no. 3, pp. 1035-1056, Ingenta.  
  2. Neural reconstruction of Lorenz attractors by an observable
    Cannas, B.; Cincotti, S.
    Chaos, Solitons and Fractals, v 14, n 1, July, 2002, p 81-86, Compendex.
  3. Fluctuational Escape from a Quasi-Hyperbolic Attractor in the Lorenz System
    Anishchenko, V. S.; Luchinsky, D. G.; McClintock, P. V. E.; Khovanov, I. A.; Khovanova, N. A.
    Journal of Experimental and Theoretical Physics, 2002, vol. 94, no. 4, pp. 821-833, Ingenta.  
  4. Experimental Verification of the Butterfly Attractor in a Modified Lorenz System
    Ozoguz, S.; Elwakil, A. S.; Kennedy, M. P.
    International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2002, vol. 12, no. 7, pp. 1627-1632, Ingenta.  
  5. Creation of a complex butterfly attractor using a novel Lorenz-type system
    Elwakil, A.S.; Ozoguz, S.; Kennedy, M.P.
    IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, v 49, n 4, April, 2002, p 527-530, Compendex.
  6. Noise-induced escape from the Lorenz attractor.
    Anishchenko, V. S.; Khovanov, I. A.; Khovanova, N. A.; Luchinsky, D. G.; McClintock, P. V. E.
    Fluct. Noise Lett. 1 (2001), no. 1, L27--L33, MathSciNet.
  7. Lattice Bhatnagar-Gross-Krook model for the Lorenz attractor
    Yan, G.; Yuan, L.
    Physica D: Nonlinear Phenomena, v 154, n 1-2, Jun 1, 2001, p 43-50, Compendex.
  8. Effects of atomic coherences and injected field on the dynamics of generalized Lorenz-Haken equation
    Deng, X. L.; Ma, H. Q.; Chen, B. D.; Huang, H. B.
    Physics Letters A, 2001, vol. 290, no. ER1-2, pp. 77-80, Ingenta.  
  9. Attractors estimate and existence of homoclinic orbits in the Lorenz system
    Leonov, G.A.
    Prikladnaya Matematika i Mekhanika, v 65, n 1, 2001, p 21035, Compendex.
  10. A New View of the Lorenz Attractor
    Magnitskii, N. A.; Sidorov, S. V.
    Differential Equations, 2001, vol. 37, no. 11, pp. 1568-1579, Ingenta.  
  11. The Lorenz equation as a metaphor for the Navier-Stokes equations
    Foias, C.; Jolly, M. S.; Kukavica, I.; Titi, E. S.
    Discrete and Continuous Dynamical Systems, 2001, vol. 7, no. 2, pp. 403-430, Ingenta.  
  12. Chaos in the Lorenz Equations: A Computer Assisted Proof Part III: Classical Parameter Values
    Konstantin Mischaikow, Marian Mrozek, Andrzej Szymczak  
    Journal of Differential Equations, Vol. 169, No. 1, Jan 2001, pp. 17-56, Ideal.  
  13. What's new on Lorenz strange attractors?  
    Viana, Marcelo
    Math. Intelligencer 22 (2000), no. 3, 6--19, MathSciNet.
  14. Mathematics: The Lorenz attractor exists  
    Stewart, Ian
    Nature, 2000, vol. 406, no. 6799, pp. 948, Ingenta.  
  15. Nonsymmetric Lorenz attractors from a homoclinic bifurcation  
    Robinson, Clark   
    SIAM J. Math. Anal. 32 (2000), no. 1, 119--141 (electronic), Math. Sci. Net.
  16. The Effect of Incubation Time Distribution on the Extinction Characteristics of a Rabies Epizootic
    A. C. Fowler
    Bulletin of Mathematical Biology, Vol. 62, No. 4, Jul 2000, pp. 633-655, Ideal.  
  17. Derivation of stochastic oscillator of the Duffing type from Lorenz equation and identification of the limit process.
    Narita, Kiyomasa
    Surikaisekikenkyusho Kokyuroku No. 1157 (2000), 74--89, MathSciNet.
  18. The Lorenz attractor exists  
    Tucker, Warwick
    C. R. Acad. Sci. Paris Sér. I Math. 328 (1999), no. 12, 1197--1202, Math. Sci. Net.
  19. A nonlinear feedback control of the Lorenz equation.
    Hwang, C.-C.; Fung, R.-F.; Li, W.-J.
    International journal of engineering science, 1999, vol. 37, no. 14, pp. 1893, Ingenta.  
  20. Feasibility study of extended range atmospheric prediction through time average Lorenz attractor.
    Pal, Pradip K.; Shah, Shivani
    Indian journal of radio & space physics, 1999, vol. 28, no. 6, pp. 271, Ingenta.  
  21. Chaos and Peak-to-Peak Dynamics in a Plankton-Fish Model
    Sergio Rinaldi, Cosimo Solidoro
    Theoretical Population Biology, Vol. 54, No. 1, Aug 1998, pp. 62-77, Ideal.  
  22. Lorenz attractors with arbitrary expanding dimension
    Bonatti, Christian; Pumariño, António; Viana, Marcelo   
    C. R. Acad. Sci. Paris Sér. I Math. 325 (1997), no. 8, 883--888, Math. Sci. Net.
  23. On Spurious Fixed Points of Runge-Kutta Methods
    F. Vadillo
    Journal of Computational Physics, Vol. 132, No. 1, Mar 1997, pp. 78-90, Ideal.  
  24. On a class of nonlocal bifurcation concerning the Lorenz attractor  
    Qi, Dongwen   
    A Chinese summary appears in Acta Math. Sinica {40} (1997), no. 1, 155.  Acta Math. Sinica (N.S.) 12 (1996), no. 1, 54--70, Math. Sci. Net.
  25. The random attractor of the stochastic Lorenz system.
    Schmalfuß, Björn
    Z. Angew. Math. Phys. 48 (1997), no. 6, 951--975, MathSciNet.
  26. Boundedness of attractors in the complex Lorenz model
    Toronov, Vladislav Yu.; Derbov, Vladimir L.
    Physical Review E. Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, v 55, n 3-B, Mar, 1997, p 3689, Compendex.
  27. Integrals of motion and the shape of the attractor for the Lorenz model.
    Giacomini, H.; Neukirch, S.
    Phys. Lett. A 227 (1997), no. 5-6, 309--318, MathSciNet.
  28. Numerical Study of Lorenz's Equation by the Adomian Method.
    Guellal, S.; Grimalt, P.; Cherruault, Y.
    Computers & mathematics with applications, 1997, vol. 33, no. 3, pp. 25, Ingenta.  
  29. Spatial Chaotic Structure of Attractors of Reaction-Diffusion Systems  
    V. Afraimovich, A. Babin, S.-N. Chow  
    Transactions of the American Mathematical Society, Vol. 348, No. 12. (Dec., 1996), pp. 5031-5063, Jstor.  
  30. Lorenz attractor through saddle-node bifurcations  
    Morales, C. A.
    Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996), no. 5, 589--617, Math. Sci. Net.
  31. A Shooting Approach to Chaos in the Lorenz Equations
    S. P. Hastings, W. C. Troy
    Journal of Differential Equations, Vol. 127, No. 1, May 1996, pp. 41-53, Ideal.  
  32. Generalized Lorenz-Type Systems
    Mostafa A. Abdelkader
    Journal of Mathematical Analysis and Applications, Vol. 199, No. 1, Apr 1996, pp. 1-13, Ideal.  
  33. Bifurcation Structure of Lorenz-Type Five-Equation Model in Thermal Convection.
    Ilda, Sei-ichi; Ogawara, Kakuji
    JSME international journal. Series II, Fluids engineering, heat transfer, power, combustion, thermophysical properties, 1996, vol. 39, no. 1, pp. 36, Ingenta.  
  34. Forced Lorenz attractor and the feasibility of drought and excess rainfall prediction
    Pal, P. K.
    Indian Journal of Radio & Space Physics, v 25, n 4, 1996, p 175, Compendex.
  35. Corrigendum: On the shape and dimension of the Lorenz attractor  
    Doering, Charles R.; Gibbon, J. D.
    [Dynam. Stability Systems {10} (1995), no. 3, 255--268, Math. Sci. Net.
  36. On the shape and dimension of the Lorenz attractor
    Doering, Charles R.; Gibbon, J.D.
    Dynamics and Stability of Systems, v 10, n 3, 1995, p 255-268, Compendex.
  37. On the Strange Attractor and Transverse Homoclinic Orbits for the Lorenz Equations
    H. Spreuer, E. Adams
    Journal of Mathematical Analysis and Applications, Vol. 190, No. 2, Mar 1995, pp. 329-360, Ideal.
  38. Convergence of psi-series solutions of the Duffing equation and the Lorenz system.
    Melkonian, S.; Zypchen, A.
    Nonlinearity 8 (1995), no. 6, 1143--1157, MathSciNet.
  39. Structural similarities and differences among attractors and their intensity maps in the laser-Lorenz model
    Abraham, N.B.; Allen, U.A.; Peterson, E.; Vicens, A.; Vilaseca, R.; Espinosa, V.; Lippi, G.L.
    Optics Communications, v 117, n 3-4, Jun 1, 1995, p 367-384, Compendex.  
  40. Characterization of strange attractors of Lorenz model of general circulation of the atmosphere
    Masoller, C.; Schifino, A.C. Sicardi; Romanelli, L.
    Chaos, Solitons and Fractals, v 6, n Suppl, 1995, p 357, Compendex.
  41. Nonlinear Forecasting of Non-Uniform Chaotic Attractors in an Enzyme Reaction  
    L. F. Olsen, K. R. Valeur, T. Geest, C. W. Tidd, W. M. Schaffer  
    Philosophical Transactions: Physical Sciences and Engineering, Vol. 348, No. 1688, Chaos and Forecasting. (Sep. 15, 1994), pp. 421-430, Jstor.
  42. Periodic orbit analysis of the Lorenz attractor  
    Eckhardt, Bruno; Ott, Gerolf   
    Z. Phys. B 93 (1994), no. 2, 259--266, Math. Sci. Net.
  43. A Proof That the Lorenz Equations Have a Homoclinic Orbit
    S.P. Hastings, W.C. Troy
    Journal of Differential Equations, Vol. 113, No. 1, Oct 1994, pp. 166-188, Ideal.  
  44. Nonlinear feedback for controlling the Lorenz equation.
    Alvarez-Ramirez, Jose
    Physical review. E. Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1994, vol. 50, no. 3, pp. 2339, Ingenta.  
  45. Ensembles of the Lorenz Attractor  
    A. P. Rothmayer, D. W. Black  
    Proceedings: Mathematical and Physical Sciences, Vol. 441, No. 1912. (May 8, 1993), pp. 291-312, Jstor.  
  46. New Treatment on Bifurcations of Periodic Solutions and Homoclinic Orbits at High r in the Lorenz Equations  
    Jibin Li, Jianming Zhang  
    SIAM Journal on Applied Mathematics, Vol. 53, No. 4. (Aug., 1993), pp. 1059-1071, Jstor.  
  47. Normal forms and Lorenz attractors  
    Shil'nikov, A. L.; Shil'nikov, L. P.; Turaev, D. V.  
    Internat. J. Bifur. Chaos Appl. Sci. Engrg. 3 (1993), no. 5, 1123--1139, Math. Sci. Net.
  48. The dynamics of perturbations of the contracting Lorenz attractor  
    Rovella, Alvaro   
    Bol. Soc. Brasil. Mat. (N.S.) 24 (1993), no. 2, 233--259, Math. Sci. Net.
  49. Chaos in Ecology: Is Mother Nature a Strange Attractor?  
    Alan Hastings, Carole L. Hom, Stephen Ellner, Peter Turchin, H. Charles J. Godfray  
    Annual Review of Ecology and Systematics, Vol. 24. (1993), pp. 1-33, Jstor.  
  50. Characterization of the Lorenz attractor by unstable periodic orbits  
    Franceschini, Valter; Giberti, Claudio; Zheng, Zhi Ming
    Nonlinearity 6 (1993), no. 2, 251--258, Math. Sci. Net.
  51. "Lorenz attractor" from differential equations with piecewise-linear terms
    Baghious, E. H.; Jarry, P.
    Internat. J. Bifur. Chaos Appl. Sci. Engrg. 3 (1993), no. 1, 201--210, Math. Sci. Net.
  52. On bifurcations of the Lorenz attractor in the Shimizu-Morioka model
    Shil'nikov, Andrey L.
    Homoclinic chaos (Brussels, 1991). Phys. D 62 (1993), no. 1-4, 338--346, Math. Sci. Net.
  53. On the multifractal character of the Lorenz attractor.
    Domínguez-Tenreiro, R.; Roy, L. J.; Martínez, V. J.
    Progr. Theoret. Phys. 87 (1992), no. 5, 1107--1118, Math. Sci. Net.
  54. On degenerate singularities that generate geometric Lorenz attractors. (Japanese)  
    Dumortier, F.; Kokubu, Hiroshi; Oka, Hiroe
    Topics around chaotic dynamical systems (Japanese) (Kyoto, 1992), Math. Sci. Net.
  55. On the boundaries of the domain of existence of the Lorenz attractor.
    Bykov, V.V.; Shil'nikov, A.L.
    Selecta mathematica Sovietica, 1992, vol. 11, no. 4, pp. 375, Ingenta.  
  56. On the Existence of a Lorenz Strange Attractor in Magnetospheric Convection Dynamics.
    Summers, Danny; Mu, Jian-lin
    Geophysical research letters., 1992, vol. 19, no. 19, pp. 1899, Ingenta.  
  57. Homoclinic Bifurcation to a Transitive Attractor of Lorenz Type, II.
    Robinson, Clark
    SIAM journal on mathematical analysis, 1992, vol. 23, no. 5, pp. 1255, Ingenta.  
  58. A topological invariant of the Lorenz attractor. (Russian)  
    Klinshpont, N. È.
    Uspekhi Mat. Nauk 47 (1992), no. 2(284),195--196 translation in Russian Math. Surveys 47 (1992), no. 2, 221--223, Math. Sci. Net.
  59. Dissipative hydrodynamic oscillators. VII. The two-component Lorenz model as a Duffing oscillator, and integrability.
    Sanjuán, M. A. F.; Valero, J. L.; Velarde, M. G.
    Nuovo Cimento D (1) 13 (1991), no. 7, 913--918, MathSciNet.
  60. Lorenz attractors through Sil'nikov-type bifurcation  
    Rychlik, Marek Ryszard  
    I. Ergodic Theory Dynam. Systems 10 (1990), no. 4, 793--821, Math. Sci. Net.
  61. Co-existing periodic attractors in the Lorenz equations.
    Nolte, Klaus-Georg
    C. R. Math. Rep. Acad. Sci. Canada 12 (1990), no. 6, 229--234, MathSciNet.
  62. Attractor properties of laser dynamics. A comparison of NH3-laser emission with the Lorenz model
    Li, M.Y.; Win, Tin; Weiss, C.O.; Heckenberg, N.R.
    Optics Communications, v 80, n 2, Dec 15, 1990, p 119-126, Compendex.
  63. A Note on the Differential Equations of Gleick-Lorenz  
    Morris W. Hirsch  
    Proceedings of the American Mathematical Society, Vol. 105, No. 4. (Apr., 1989), pp. 961-962, Jstor.  
  64. Homoclinic bifurcation to a transitive attractor of Lorenz type.
    Robibinson, C.
    Nonlinearity, 1989, vol. 2, no. 4, pp. 495, Ingenta.  
  65. Autoregressive methods for chaos on binary sequences for the Lorenz attractor.
    Singh, P.; Joseph, D.D.
    Physics letters, 1989, vol. 135, no. 4/5, pp. 247, Ingenta.  
  66. Chaos, Strange Attractors, and Fractal Basin Boundaries in Nonlinear Dynamics  
    Celso Grebogi, Edward Ott, James A. Yorke  
    Science, New Series, Vol. 238, No. 4827. (Oct. 30, 1987), pp. 632-638, Jstor.  
  67. Lorenz cross sections of the chaotic attractor of the double rotor.
    Kostelich, Eric J.; Yorke, James A.
    Phys. D 24 (1987), no. 1-3, 263--278, MathSciNet.
  68. Strange Attractors of Uniform Flows  
    Ittai Kan  
    Transactions of the American Mathematical Society, Vol. 293, No. 1. (Jan., 1986), pp. 135-159, Jstor.  
  69. On the Nature of the Torus in the Complex Lorenz Equations  
    A. C. Fowler, M. J. McGuinness  
    SIAM Journal on Applied Mathematics, Vol. 44, No. 4. (Aug., 1984), pp. 681-700, Jstor.  
  70. Intermediate model solutions to the Lorenz equations: strange attractors and other phenomena.
    Gent, Peter R.; McWilliams, James C.
    J. Atmospheric Sci. 39 (1982), no. 1, 3--13, MathSciNet.
  71. Ordinary Differential Equations with Strange Attractors  
    C. J. Marzec, E. A. Spiegel  
    SIAM Journal on Applied Mathematics, Vol. 38, No. 3. (Jun., 1980), pp. 403-421, Jstor.  
  72. Periodic Solutions and Bifurcation Structure at High R in the Lorenz Model  
    K. A. Robbins  
    SIAM Journal on Applied Mathematics, Vol. 36, No. 3. (Jun., 1979), pp. 457-472, Jstor.  
  73. New interpretation and size of strange attractor of the Lorenz model of turbulence.
    Haken, H.; Wunderlin, A.
    Phys. Lett. A 62 (1977), no. 3, 133--134, MathSciNet.
  74. Computer pictures of the Lorenz attractor.
    Lanford, Oscar E., III
    Turbulence Seminar (Univ. Calif., Berkeley, Calif., 1976/1977), pp. 113--116. Lecture Notes in Math., Vol. 615, Springer, Berlin, 1977, MathSciNet.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004