Astrophysical stochastic models

In the foregoing sections we reviewed some stochastic models for stellar formation and galactic evolution widely employed in the literature. Here, we shall discuss expUdtly a simplified astrophysical model where the stochastic processes introduced for mimicking the complexity of the relevant interactions are dealt with by recourse to the analytical tools of the previous chapters in this volume (notably Grigolini and Marchesoni, Chapter II). 

The astrophysical problem of justifying on theoretical grounds the morphology of galaxies (spiral and eUiptical, with their different content in stars and gas), their chemical evolution (initial rapid enrichment of metals, i.e., any element heavier than hydrogen and helium), and, finally, the attempt to trace a classification based on different physical aspects of the evolution, has been tackled by employing the approach of cooperative systems. In these models a scenario is proposed where the large-scale dynamics are related to the local microscopic interactions. At the same time a macroscopic description (e.g., the interplay of various phases, the metallicity) is derived by means of few (stochastic) variables. 

Nonlinear dynamics of complex processes is an active research field with large numbers of publications in basic research and broad applications from diverse fields of science. Nonlinear dynamics as manifested by deterministic and stochastic evolution models of complex behaviour has entered statistical physics, physical chemistry, biophysics, geophysics, astrophysics, theoretical ecology, semiconductor physics and -optics etc. This research has induced a new terminology in science connected with new questions, problems, solutions and methods. New scenarios have emerged for spatio-temporal structures in dynamical systems far from equilibrium. Their analysis and possible control are intriguing and challenging aspects of the current research. 

---