Biomedical subjects

D Pingel

Publications and source records attributed to D Pingel.

4 recordsLinked to original sources

PubMed2001

Detecting unstable periodic orbits in chaotic continuous-time dynamical systems.

We extend the recently developed method for detecting unstable periodic points of chaotic time-discrete dynamical systems to find unstable periodic orbits in time-continuous systems, given by a set of ordinary differential equations. This is achieved by the reduction of the continuous flow to a Poincaré map which is then searched for periodic points. The algorithm has global convergence properties and needs no a priori knowledge of the system. It works well for both dissipative and Hamiltonian dynamical systems which is demonstrated by exploring the Lorenz system and the hydrogen atom in a strong magnetic field. The advantages and general features of the approach are discussed in detail.

Journal Article↗

PubMed2000

Theory and applications of the systematic detection of unstable periodic orbits in dynamical systems

A topological approach and understanding to the detection of unstable periodic orbits based on a recently proposed method [Phys. Rev. Lett. 78, 4733 (1997)] is developed. This approach provides a classification of the set of transformations necessary for finding the orbits. Applications to the Ikeda and Henon map are performed, allowing a study of the distributions of Lyapunov exponents for high periods. In particular, the properties of the least unstable orbits up to period 36 are investigated and discussed.

Journal Article↗

PubMed2000

Analyzing lyapunov spectra of chaotic dynamical systems

It is shown that the asymptotic spectra of finite-time Lyapunov exponents of a variety of fully chaotic dynamical systems can be understood in terms of a statistical analysis. Using random matrix theory, we derive numerical and in particular, analytical results that provide insights into the overall behavior of the Lyapunov exponents particularly for strange attractors. The corresponding distributions for the unstable periodic orbits are investigated for comparison.

Journal Article↗

PubMed1992

Surgical versus non-surgical treatment of fractures of the articular process of the mandible.

In a clinical, radiographic and angiographic study, we reinvestigated 34 patients with dislocated fractures of the condylar neck. 20 of them had been treated by open reduction, 14 in a conservative-functional way. The clinical results were nearly equal in both groups. The instrumental registration and the X-ray findings showed considerable deviations in the joint physiology in the conservative group. 19 of 20 patients operated on showed near-anatomical reconstruction with good functional results.

Adolescent↗