Its been over 10 years, but I once wrote some code to build very detailed bifurcation plots for a system of non-linear ODEs. The big picture idea was the following:
1) The system of odes contained one or more parameters. Pick a paramter "a" and a range of values you want to vary it over.
2) In a loop, for each parameter value "a" simulate a solution using ode45 or another solver. Capture the points the solution crosses some type of poincare section using the "options" input to ode45 by setting an appropriate event. For each point, create an (x,y) pair where x = a and y = the point at which the events occur. You'll have many different pairs. For example, if your ode system is a simple oscillator, a is the frequency, and your event is every time the solution crosses the value zero, you'll have numerous crosses for each value of "a".
3) Plot all of these (x,y) pairs that will show you the character of the event crosses as a function of the parameter "a".
If you want to build a UI around it, its no different than building any other UI in MATLAB.
If you're trying to understand the dynamics of a complex system without closed form solution, this is an interesting exercise.
Have fun and good luck.