NLD Preprints
ISSN (print) 1432-2935
URN urn:nbn:de:kobv:517-series-354
Herausgegeben von
Universität Potsdam, Interdisziplinäres Zentrum für Nichtlineare Dynamik
URN urn:nbn:de:kobv:517-series-354
Herausgegeben von
Universität Potsdam, Interdisziplinäres Zentrum für Nichtlineare Dynamik
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Keywords
- aerosol size distribution (2)
- inversion (2)
- Ill-posed problem (1)
- MHD-equations (1)
- Multiwavelength LIDAR (1)
- Planetary Rings (1)
- SPECT (1)
- Tikhonov regularization (1)
- aerosol distribution (1)
- approximate inertial manifolds (1)
- attenuated Radon transform (1)
- coated and absorbing aerosols (1)
- ill-posed problem (1)
- inverse ill-posed problem (1)
- mollifier method (1)
- multilayered coated and absorbing aerosol (1)
- multiwavelength Lidar (1)
- multiwavelength lidar (1)
- new recursive algorithm (1)
- nonlinear invers problem (1)
- nonlinear optimization (1)
- tomogrphy (1)
- variable projection method (1)
Institute
2
Strange nonchaotic attractors typically appear in quasiperiodically driven nonlinear systems. Two methods of their characterization are proposed. The first one is based on the bifurcation analysis of the systems, resulting from periodic approximations of the quasiperiodic forcing. Secondly, we propose th characterize their strangeness by calculating a phase sensitivity exponent, that measures the sensitivity with respect to changes of the phase of the external force. It is shown, that phase sensitivity appears if there is a non-zero probability for positive local Lyapunov exponents to occur.
1
We have studied bifurcation phenomena for the incompressable Navier-Stokes equations in two space dimensions with periodic boundary conditions. Fourier representations of velocity and pressure have been used to transform the original partial differential equations into systems of ordinary differential equations (ODE), to which then numerical methods for the qualitative analysis of systems of ODE have been applied, supplemented by the simulative calculation of solutions for selected initial conditions. Invariant sets, notably steady states, have been traced for varying Reynolds number or strength of the imposed forcing, respectively. A complete bifurcation sequence leading to chaos is described in detail, including the calculation of the Lyapunov exponents that characterize the resulting chaotic branch in the bifurcation diagram.