Qualitative evolution in higher-loop string cosmology

We investigate the evolution of the homogeneous and isotropic universe within the framework of the effective string gravity with string-loop modifications of dilaton couplings. In the case of barotropic perfect fluid as a nongravitational source the set of cosmological equations is presented in the form of the third-order autonomous dynamical system. The cases are considered when this system is integrable in terms of integrals depending on dilaton coupling functions. Without specifying these functions we describe generic evolution of the universe, using dynamical systems methods. The critical points and their stability are found for all regions of the parameters. The qualitatively different phase space diagrams are presented for the spatially-flat, closed and open universes. The case of the tree-level models is considered separately. The issue of dilaton stabilization is discussed within the framework of Damour-Polyakov mechanism. PUCS numbers: 9880H, 9880B, 9880C