Resource Letter: ND-1: Nonlinear Dynamics

This Resource Letter provides an introductory guide to the literature on nonlinear dynamics. Journal articles and books are cited for the following topics: general aspects of nonlinear dynamics and applications of nonlinear dynamics to various fields of physics, other sciences, and a few areas outside the sciences. Software and Internet resources are given also.

[1]  S. C. Pope,et al.  The chaotic behavior of the leaky faucet , 1985 .

[2]  Farmer,et al.  Predicting chaotic time series. , 1987, Physical review letters.

[3]  W. Brock,et al.  Is the business cycle characterized by deterministic chaos , 1988 .

[4]  John F. Lindner,et al.  Self‐organized criticality: An experiment with sandpiles , 1993 .

[5]  Tang,et al.  Type-III intermittency of a laser. , 1991, Physical Review A. Atomic, Molecular, and Optical Physics.

[6]  Nicholas B. Tufillaro,et al.  Nonlinear and chaotic string vibrations , 1989 .

[7]  Peter V. Coveney,et al.  Frontiers of Complexity: The Search for Order in a Chaotic World, Peter Coveney and Roger Highfield. 1995. Random House, Inc., New York, NY. 480 pages. ISBN: 0-449-90832-1. $27.50 , 1996 .

[8]  Maître,et al.  Flowerlike patterns generated by a laser beam transmitted through a rubidium cell with single feedback mirror. , 1994, Physical review letters.

[9]  Libchaber,et al.  Fixed winding number and the quasiperiodic route to chaos in a convective fluid. , 1985, Physical review letters.

[10]  Leon Glass,et al.  Nonlinear dynamics of physiological function and control. , 1991, Chaos.

[11]  Carroll,et al.  Experimental and Numerical Evidence for Riddled Basins in Coupled Chaotic Systems. , 1994, Physical review letters.

[12]  Troy Shinbrot,et al.  Progress in the control of chaos , 1995 .

[13]  Bernardo A. Huberman.  AN ECOLOGY OF MACHINES , 1989 .

[14]  Gay,et al.  Positive-energy spectrum of the hydrogen atom in a magnetic field. , 1991, Physical review letters.

[15]  Müller.  Nature of quantum chaos in spin systems. , 1986, Physical review. A, General physics.

[16]  S. Strogatz,et al.  Dynamics of a large system of coupled nonlinear oscillators , 1991 .

[17]  Solari,et al.  Structure of chaos in the laser with saturable absorber. , 1992, Physical review letters.

[18]  Leon Glass,et al.  Cardiac arrhythmias and circle maps-A classical problem. , 1991, Chaos.

[19]  Tufillaro.  Braid analysis of a bouncing ball. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  Riedel,et al.  Temporal sequences and chaos in neural nets. , 1988, Physical review. A, General physics.

[21]  Leon O. Chua,et al.  Simplest chaotic nonautonomous circuit , 1984 .

[22]  Paul Halpern.  Sticks and stones: A guide to structurally dynamic cellular automata , 1989 .

[23]  Paczuski,et al.  Exact results for spatiotemporal correlations in a self-organized critical model of punctuated equilibrium. , 1995, Physical review letters.

[24]  Grebogi,et al.  Experimental confirmation of the scaling theory for noise-induced crises. , 1991, Physical review letters.

[25]  Eckmann,et al.  Liapunov exponents from time series. , 1986, Physical review. A, General physics.

[26]  Steven H. Strogatz,et al.  Ordering chaos with disorder , 1995, Nature.

[27]  Schreiber,et al.  Topological time-series analysis of a string experiment and its synchronized model. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  Robert F. Cahalan,et al.  Chaotic rhythms of a dripping faucet , 1990 .

[29]  J. Scheinkman.  Nonlinearities in Economic Dynamics , 1990 .

[30]  Brown,et al.  Synchronization of chaotic systems: The effects of additive noise and drift in the dynamics of the driving. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[31]  T. Bountis.  Period doubling bifurcations and universality in conservative systems , 1981 .

[32]  Rath,et al.  Microwave ionization of hydrogen atoms: Experiment vs classical dynamics. , 1985, Physical review letters.

[33]  Ciriyam Jayaprakash,et al.  Simple models of self-organized criticality , 1995 .

[34]  Grebogi,et al.  Shadowing of physical trajectories in chaotic dynamics: Containment and refinement. , 1990, Physical review letters.

[35]  Hansel,et al.  Synchronization and computation in a chaotic neural network. , 1992, Physical review letters.

[36]  Stephen K. Scott,et al.  Oscillations, waves, and chaos in chemical kinetics , 1994 .

[37]  H. Weidenmuller,et al.  Aspects of chaos in nuclear physics , 1988 .

[38]  McCormick,et al.  Multiplicity in a chemical reaction with one-dimensional dynamics. , 1986, Physical review letters.

[39]  R A Kerr.  Pluto's Orbital Motion Looks Chaotic: The oddest planet seems to have a new distinction: its motion around the sun is irregular to the point of unpredictability. , 1988, Science.

[40]  G. Mindlin,et al.  Classification of strange attractors by integers. , 1990, Physical review letters.

[41]  E. Ott.  Strange attractors and chaotic motions of dynamical systems , 1981 .

[42]  Rodolfo Cuerno,et al.  Deterministic chaos in the elastic pendulum: A simple laboratory for nonlinear dynamics , 1992 .

[43]  Alan V. Oppenheim,et al.  Circuit implementation of synchronized chaos with applications to communications. , 1993, Physical review letters.

[44]  P. Coullet,et al.  From oscillations to excitability: A case study in spatially extended systems. , 1994, Chaos.

[45]  Giacomelli,et al.  Vortices and defect statistics in two-dimensional optical chaos. , 1991, Physical review letters.

[46]  Jess Benhabib,et al.  Chaos: Significance, Mechanism, and Economic Applications , 1989 .

[47]  J. Delos,et al.  Effect of closed classical orbits on quantum spectra: Ionization of atoms in a magnetic field. , 1987, Physical review letters.

[48]  Joseph Ford,et al.  How random is a coin toss , 1983 .

[49]  Eli Tziperman,et al.  El Ni�o Chaos: Overlapping of Resonances Between the Seasonal Cycle and the Pacific Ocean-Atmosphere Oscillator , 1994, Science.

[50]  Richards,et al.  Microwave ionization of H atoms: Breakdown of classical dynamics for high frequencies. , 1988, Physical review letters.

[51]  A. Zhabotinsky.  A history of chemical oscillations and waves. , 1991, Chaos.

[52]  Andreas S. Weigend,et al.  The Future of Time Series: Learning and Understanding , 1993 .

[53]  P. V. Elyutin.  The quantum chaos problem , 1988 .

[54]  Celso Grebogi,et al.  Using small perturbations to control chaos , 1993, Nature.

[55]  J. Ford,et al.  Does quantum mechanics obey the correspondence principle? Is it complete? , 1992 .

[56]  Carroll,et al.  Driving systems with chaotic signals. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[57]  Alan J. Hurd.  Resource Letter FR-1: Fractals , 1988 .

[58]  Roy,et al.  Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system. , 1992, Physical review letters.

[59]  M. Mitchell Waldrop,et al.  Complexity : the emerging science and the edge of order and chaos , 1992 .

[60]  Roy,et al.  Tracking unstable steady states: Extending the stability regime of a multimode laser system. , 1992, Physical review letters.

[61]  R. Holzner,et al.  Progress in the analysis of experimental chaos through periodic orbits , 1994 .

[62]  E. Hunt.  Stabilizing high-period orbits in a chaotic system: The diode resonator. , 1991 .

[63]  Grebogi,et al.  Controlling chaos in high dimensional systems. , 1992, Physical review letters.

[64]  Fedor Mitschke,et al.  Estimation of Lyapunov exponents from time series: the stochastic case , 1993 .

[65]  G. Sussman,et al.  Chaotic Evolution of the Solar System , 1992, Science.

[66]  Tang,et al.  Self-Organized Criticality: An Explanation of 1/f Noise , 2011 .

[67]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[68]  Prangé,et al.  Experimental realizations of kicked quantum chaotic systems. , 1989, Physical review letters.

[69]  W. Freeman,et al.  How brains make chaos in order to make sense of the world , 1987, Behavioral and Brain Sciences.

[70]  N. Tufillaro.  The effects of additive noise and drift in the dynamics of the driving on chaotic synchronization , 1994, chao-dyn/9411010.

[71]  Dressler,et al.  Controlling chaos using time delay coordinates. , 1992, Physical review letters.

[72]  Horseshoes in the driven, damped pendulum , 1986 .

[73]  Lee,et al.  Experimental observation of on-off intermittency. , 1994, Physical review letters.

[74]  W. Ditto,et al.  Taming spatiotemporal chaos with disorder , 1995, Nature.

[75]  Carlson,et al.  Properties of earthquakes generated by fault dynamics. , 1989, Physical review letters.

[76]  Stephen Wolfram,et al.  Cellular automata as models of complexity , 1984, Nature.

[77]  N. Tufillaro,et al.  Relative rotation rates: Fingerprints for strange attractors. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[78]  Westervelt,et al.  Fractal basin boundaries and intermittency in the driven damped pendulum. , 1986, Physical review. A, General physics.

[79]  J. Gollub,et al.  Order-disorder transition in capillary ripples. , 1989, Physical review letters.

[80]  S. Kauffman.  At Home in the Universe: The Search for the Laws of Self-Organization and Complexity , 1995 .

[81]  Swinney,et al.  Regular and chaotic chemical spatiotemporal patterns. , 1988, Physical review letters.

[82]  Jensen,et al.  Renormalization, unstable manifolds, and the fractal structure of mode locking. , 1985, Physical review letters.

[83]  Timo Hartmann,et al.  Chaos: A Program Collection for the PC , 1994 .