Nonlinear Dynamics And ChaosThis essential handbook provides the theoretical and experimental tools necessary to begin researching the nonlinear behavior of mechanical, electrical, optical, and other systems. The book describes several nonlinear systems which are realized by desktop experiments, such as an apparatus showing chaotic string vibrations, an LRC circuit displaying strange scrolling patterns, and a bouncing ball machine illustrating the period doubling route to chaos. Fractal measures, periodic orbit extraction, and symbolic analysis are applied to unravel the chaotic motions of these systems. The simplicity of the examples makes this an excellent book for undergraduate and graduate-level physics and mathematics courses, new courses in dynamical systems, and experimental laboratories. |
Contents
What is in this book? | 1 |
Dynamical Systems Theory | 4 |
Knots and Templates | 5 |
Copyright | |
21 other sections not shown
Common terms and phrases
asymptotic basins of attraction bifurcation diagram bouncing ball system braid branch calculate Chaotic dynamics chaotic motions cross section damping defined dialog box differential equations Duffing equation Duffing oscillator dynamical systems eigenvalues example experimental fixed point flow fractal frequency geometric graph homoclinic point homoclinic tangle horizontal horseshoe map hyperbolic illustrated in Figure impact map impact phase initial conditions intersection invariant set iteration knot limit set linear Mathematica mathematical matrix menu nonlinear dynamics nonlinear systems period one orbit period three orbits period two orbit periodic orbits periodic points phase space Phys planar plot Poincaré map quadratic map quasiperiodic motion reference frame relative rotation rates resonance saddle Sarkovskii's theorem sequence shown in Figure simulation stable manifold strange attractor string vibrations symbolic dynamics table's template theorem theory topological torus trajectory trapping region unit interval unstable periodic variable vector field vertical window