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The interaction of the accreting mass and the X-ray radiation of a spherically accreting neutron star is described by a discrete — time dynamical model. Its main feature consists of a nonlinear feedback mechanism between mass accretion and escaping radiation. The model is studied with respect to its stability properties and its astrophysical implications. As a function of time, we obtain stationary, periodic, and chaotic luminosities. The different kinds of behavior occur in different regimes of the mass accretion rate.

We present a phenomenological model of spherically accreting neutron stars at high mass accretion rates. The radiation and the optically thick plasma are described as two interacting fluids. The time evolution of the regarded system is calculated by a discrete time iteration map. It is shown, that the neutron star in our model may well exceed the Eddington luminosity.

This review contains a brief introduction to the terminology of deterministic chaos, and a summary of important properties and definitions of strange attractors. A method is described how to reconstruct the attractor from experimental data. Using synthetic data, the specific problems associated with the reconstruction are examined. As an observational example, analysis of data from the accreting neutron star system Her X-1 is described. Finally, we discuss the physical interpretation of these observations, the possible implications for the description of the system from a general point of view, the specific implication for the pulse shape and pulse to pulse variations, and possible approaches towards a better understanding of both accretion disc and accretion column.