And Here is The Code:

(8 points) Parabolic burster. A Parabolic burster (parath.ode,parath.m) needs two slow variables and a SNIC. The simplest way to get a SNIC is with the theta model. So here is our model: yz=1cos+(1+cos)(I0+aybz)=y=(/)z with the reset condition: each time (t) crosses , it is reset to and y is incremented by and z is incremented by /. Simulate this model (in the codes is called u ). Zoom into a burst and estimate the time between successive spikes. (In MatLab, you can get the values of the peaks by using the Tools, DataTips; in XPP, hold the mouse button or pad down and scroll in the drawing area; the x and y coordinates are at the bottom.) Show that they decrease and then increase; the charcteristic of the paraboloc burster. Finally, how big can I0 get? Describe what happens to the bursts as I0 decreases below 0.1 to I0=0.001. That is how does the width of the burst change? How does the interval between bursts change? The ratio of the width of the burst to the total period of the burst is called the duty cycle. Determine the duty cycle for I0=0.2,0.1,0.05,0.02,0.01