As per request, here is the code that I wrote to draw bifurcation plots in R. Bifurcation diagrams for discrete maps can be done using this code by James Jones. It is a little easier since approximation is not needed. In the following code, I used the deSolve library to draw bifurcation diagrams for a 
MATLAB has a nice program called pplane that draws phase planes of differential equations models. pplane on MATLAB is an elaborate program with an interactive GUI where you can just type the model to draw the phase planes. The rest you fidget by clicking (to grab the initial conditions) and it draws the dynamics automatically. 
So many know about the Lotka-Volterra model (i.e. the predator-prey model) in ecology. This model portrays two species, the predator (y) and the prey (x), interacting each other in limited space. The prey grows at a linear rate () and gets eaten by the predator at the rate of (). The predator gains a certain 
Zero Inflated Models and Generalized Linear Mixed Models with R.
Zuur, Saveliev, Ieno (2012).
