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. |
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Page 19
... map △ , ( x ) . For μ = 1 we have | A ′ ( x ) | = 2 for all x E [ 0,1 ] , and thus λ ( x ) = In 2. This is consistent with the result of the previous section , where we found f " ( xo + ) - f " ( xo ) ... Logistic Map 19 The Logistic Map.
... map △ , ( x ) . For μ = 1 we have | A ′ ( x ) | = 2 for all x E [ 0,1 ] , and thus λ ( x ) = In 2. This is consistent with the result of the previous section , where we found f " ( xo + ) - f " ( xo ) ... Logistic Map 19 The Logistic Map.
Page 60
... logistic map also readily displays an intermittent transistion to chaos . Figure 3.14 shows the logistic map iterates for the map parameter μ in the neighborhood of μe = 1 + 2√2 = 3.828 ... , which is the value of μ for the onset of ...
... logistic map also readily displays an intermittent transistion to chaos . Figure 3.14 shows the logistic map iterates for the map parameter μ in the neighborhood of μe = 1 + 2√2 = 3.828 ... , which is the value of μ for the onset of ...
Page 64
... logistic map is obtained . The logistic map ( 2.14 ) serves as the archetype map leading to period doubling and through functional iteration leads us to the universal map asso- ciated with the period - doubling transistion to chaos ...
... logistic map is obtained . The logistic map ( 2.14 ) serves as the archetype map leading to period doubling and through functional iteration leads us to the universal map asso- ciated with the period - doubling transistion to chaos ...
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