Chaotic Dynamics of Nonlinear SystemsProvided here is the first introductory book on chaos in nonlinear systems written for senior and first year graduate students in physics and science. The book does not attempt to be encyclopedic, but instead covers those topics that have become standard in the subject. Its level should make the book appealing to a broad variety of scientists and engineers as an introduction to Chaotic Dynamics. The book has many examples and is heavily illustrated. It has been designed specifically for senior and first-year graduates concerned with chaos and nonlinear systems. |
From inside the book
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Page 123
... damped , driven pendulum has also been modeled with an electronic circuit , which then serves as an analog device to explore extensively the dynamical behavior of this system . We refer specifically to D ... Damped , Driven Pendulum 123.
... damped , driven pendulum has also been modeled with an electronic circuit , which then serves as an analog device to explore extensively the dynamical behavior of this system . We refer specifically to D ... Damped , Driven Pendulum 123.
Page 124
... pendulum . In any system like the driven , damped pendulum , the various choices of the parameters can be very important for determining the behavior of the system . If the construction or operation of a device is at issue , then ...
... pendulum . In any system like the driven , damped pendulum , the various choices of the parameters can be very important for determining the behavior of the system . If the construction or operation of a device is at issue , then ...
Page 128
... damped pendulum illustrate some of the complexities contained in such nonlinear oscillators . The dynamic behavior and attracting sets varies greatly with differing choices for the system parameters , and further with dif- fering ...
... damped pendulum illustrate some of the complexities contained in such nonlinear oscillators . The dynamic behavior and attracting sets varies greatly with differing choices for the system parameters , and further with dif- fering ...
Contents
Introduction | 1 |
OneDimensional Maps | 13 |
Universality Theory | 33 |
Copyright | |
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Common terms and phrases
area-preserving Arnold attracting set center manifold chaotic dynamics chapter computation consider constant coordinates corresponding curves cycle elements damped pendulum dcap defined denote Df(x differential equations digits discussed disk dynamo dynamical system eigenvalues eigenvectors example Feigenbaum FIGURE finite fixed point flip bifurcation flow fractal dimension frequency given Hénon map Hopf bifurcation initial conditions initial point integrable intermittency intersection iterations laminar phase limit cycle linear logistic map Lorenz system Lyapunov exponent LZ complexity map parameter measure nonlinear obtain one-dimensional maps period-doubling periodic orbit perturbation phase space Phys plot Poincaré map Poincaré section random refer renormalization resonance scaling self-similar sequence shows simple pendulum sketch solution stable strange attractor string supercycle surface tent map theorem trajectory transformation transistion to chaos trapping region two-dimensional maps universal function unstable manifold variables vector field Xn+1 zero