  We examine the full nonlinear dynamics of closed FRW universes in the
framework of D-branes formalism. Friedmann equations contain additional terms
arising from the bulk-brane interaction that provide a concrete model for
nonsingular bounces in the early phase of the universe. We construct
nonsingular cosmological scenarios sourced with perfect fluids and a massive
inflaton field which are past eternal, oscillory and may emerge into an
inflationary phase due to nonlinear resonance mechanisms. Oscillatory behaviour
becomes metastable when the system is driven into a resonance window of the
parameter space of the models, with consequent break-up of KAM tori that trap
the inflaton, leading the universe to the inflationary regime. A construction
of the resonance chart of the models is made. Resonance windows are labeled by
an integer $n \geq 2$, where $n$ is related to the ratio of the frequencies in
the scale factor/scalar field degrees of freedom. They are typically small
compared to volume of the whole parameter space, and we examine the constraints
imposed by nonlinear resonance in the physical domain of initial configurations
so that inflation may be realized. We discuss the complex dynamics arising in
this pre-inflationary stage, the structural stability of the resonance pattern
and some of its possible imprints in the physics of inflation. We also approach
the issue of initial configurations that are connected to a chaotic exit to
inflation. Pure scalar field bouncing cosmologies are constructed. Contrary to
models with perfect fluid components, the structure of the bouncing dynamics is
highly sensitive to the initial amplitude and to the mass of the inflaton;
dynamical potential barriers allowing for bounces appear as a new feature of
the dynamics.
