  In this article we perform dynamical analysis of a broad class of barotropic
fluids in the spatially curved Friedmann-Robertson-Walker (FRW) spacetime
background without considering the cosmological constant. The first part of our
study concerns the dynamics of a fluid with an unspecified barotropic equation
of state (EoS) having as the only assumption the non-negativity of the fluid's
energy density. After defining a new set of dimensionless variables and a new
evolution parameter, we introduce the function $\Gamma$ that encodes the EoS.
In this general setup several features of the system are identified: critical
points, invariant subsets and the characteristics of the function $\Gamma$,
along with their cosmological interpretations. The second part of our work
provides two examples with specific $\Gamma$ functions. In the first example we
provide a $\Gamma$ function and then we exhibit how it can be trimmed down to a
specific class of EoS through physical arguments, while in the second example
we discuss the quadratic EoS studied in Phys.Rev. D {\bf 74}, 023523 (2006) by
comparing our approach with their analysis.
