Chaotic Dynamics: An IntroductionCambridge University Press, 26/01/1996 - 256 páginas The previous edition of this text was the first to provide a quantitative introduction to chaos and nonlinear dynamics at the undergraduate level. It was widely praised for the clarity of writing and for the unique and effective way in which the authors presented the basic ideas. These same qualities characterize this revised and expanded second edition. Interest in chaotic dynamics has grown explosively in recent years. Applications to practically every scientific field have had a far-reaching impact. As in the first edition, the authors present all the main features of chaotic dynamics using the damped, driven pendulum as the primary model. This second edition includes additional material on the analysis and characterization of chaotic data, and applications of chaos. This new edition of Chaotic Dynamics can be used as a text for courses on chaos for physics and engineering students at the second- and third-year level. |
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Índice
| 8 | |
| 39 | |
| 74 | |
CHAPTER FIVE The characterization of chaotic attractors | 109 |
CHAPTER SIX Experimental characterization prediction | 133 |
CHAPTER SEVEN Chaos broadly applied | 166 |
snowflakes | 181 |
Further reading | 190 |
Appendix B Computer program listings | 196 |
Solutions to selected problems | 242 |
Index | 253 |
Outras edições - Ver tudo
Chaotic Dynamics: An Introduction Gregory L. Baker,Jerry P. Gollub Pré-visualização indisponível - 1996 |
Chaotic Dynamics: An Introduction Gregory L. Baker,Jerry P. Gollub Pré-visualização indisponível - 1996 |
Palavras e frases frequentes
algorithm angular velocity basins of attraction bifurcation diagram calculation CALL ADDLEGEND CALL CALL CALL CALL DATAGRAPH CALL SETXSCALE Cantor set chaotic attractor chaotic behavior chaotic dynamics chaotic pendulum chaotic systems Chapter circle map complex coordinates correlation dimension corresponding damping differential equations dissipative divergence drive cycles driven pendulum dynamical systems embedding dimension End IF LET end sub entropy example experimental data FINNUM fixed point fluid Fourier fractal frequency function graph GRAPHPoint illustrated infinite number initial conditions INITNUM INPUT PROMPT INPUT PROMPT"INPUT interval iteration Kolmogorov entropy laser LET xreal linear logistic map Lyapunov exponents method nonlinear dynamics number of points orbits oscillation oſt parameters period doubling phase diagram phase plane phase space PLOT Poincaré section power spectrum prediction PRINT reconstructed attractor region saddle point shown in Figure shows simulation spatio-temporal chaos tstep two-dimensional unstable values vector winding number ximag XINT xnew
Passagens conhecidas
Página 18 - The condition for a nontrivial solution is the vanishing of the determinant of the coefficients of A and B.
Página 118 - ... have to resort to some dynamical measure - the method is known as the Lyapunov exponent. The basic idea of the Lyapunov exponent is to measure the average rate of the divergence for the neighboring trajectories on the attractor. The direction of the maximum divergence or convergence locally changes on the attractor. The motion must be monitored at each point along the trajectory. Therefore, a small sphere is defined, whose center is a given point on the attractor and whose surface consists of...
Página 112 - The typical number of neighbors of a given point will vary more rapidly with distance from that point if the set has high dimension than otherwise.
Página 4 - The angular velocity of the forcing, a>D, may be different from the natural frequency of the pendulum. In order to minimize the number of adjustable parameters the equation may be rewritten in dimensionless form as...
Página 113 - L1.2 1.4 1.6 1.8 2.0 2.0 method; each point has a circle of radius R drawn around it, and then all points within all circles of size R contribute to C(R).
Página 98 - Each crossing is mapped into another one closer to the saddle point, leading to an infinite number of intersections /2, /3, and so forth. The resulting configuration is called a heteroclinic tangle. (If Ws and W...
Página 112 - Heaviside function simply counts the number of points within a radius R of the point denoted by x,, and C(R) gives the average fraction of points within R.
Página 10 - The energy conserving feature ensures that each point rotates at a constant radius because the energy of the oscillator is proportional to the square of the radius.
Página 64 - The bifurcation diagram provides a summary of the essential dynamics and is therefore a useful method of acquiring this overview.
Página 165 - They are: (7.1) dD/df = where K is the decay rate in the laser cavity due to beam transmission, y...
Referências a este livro
Informação bibliográfica
| Título | Chaotic Dynamics: An Introduction |
| Autores | Gregory L Baker, Gregory L. Baker, Jerry P. Gollub |
| Edição | ilustrada, reimpressão, revista |
| Editora | Cambridge University Press, 1996 |
| ISBN | 0521476852, 9780521476850 |
| Número de páginas | 256 páginas |
| Exportar citação | BiBTeX EndNote RefMan |