We investigate a class of Cardassian scenarios of the universe evolution in notions of the qualitative theory of dynamical systems .
This theory allows us to analyze all solutions for all possible initial conditions on the phase plane .
In the Cardassian models we find that big-rip singularities are present as a typical behavior in the future if n < 0 .
Some exact solutions for the flat Cardassian models as well as a duality relation were found .
In turn from the statistical analysis of Knop ’ s SNIa data , without any priors on matter content in the model , we obtain that at the 99 \% confidence level this big-rip scenario will reach .
The potential function for the Hamiltonian description of dynamics is reconstructed from the SNIa data ( inverse dynamical problem ) .
We also pointed out the statistical analysis results depend oversensitively on the choice of the model parameter \mathcal { M } .