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Encounter with Chaos: Self-Organized Hierarchical Complexity in ...
Joachim Peinke,Jürgen Parisi,Otto E. Rössler,Ruedi Stoop
No preview available - 1992
algorithm amplitude analogous bias current bifurcation point breakdown calculated Cantor set chaos characteristic characterized charge carriers circle map corresponding current filament curve denotes dependence differential equation dynamical map dynamical system eigenvalues electric field embedding dimension entropy evaluation example experimental data experimental systems following constant parameters fractal dimensions frequency Henon map Hopf bifurcation initial conditions intermittency laminar phases limit cycle linear load resistance logistic map Lyapunov exponents magnetic field measure mode-locked NMR laser nonlinear dynamics observed obtained oscillatory partial voltage periodic oscillation perturbation term phase portrait phase space phase transition pitchfork bifurcation plotted Poincare cross section power spectrum present quasiperiodic radius region return map saddle node bifurcation sample sketched scaling behavior scaling function Schematic semiconductor semiconductor system shown in Fig sketched in Fig spatial stable fixed point structural stability temperature Tb trajectories transverse magnetic field two-dimensional unstable manifold values variable volume elements zero