Predator-Prey Model: Solving Equations & Plotting Results

[2slowtogofast]

I modeled these equations

dR/dt = aR - bRF

dF/dt = bRF - cF where b = b<sub>o*exp(-0.01*t*log(F))

my plots show in the beginginng the normal predator prey relationship one species is incresing the other decreasing then the first one peaks and start decreeasing while the other starts increasing, but then that stops and the both grow exponetially. Is this possible or do you think there is a problem with my code. i'll attach a figure</sub>

 

[2slowtogofast]

so my main question is if b decreases what should happen. its easy to see in the first equation that the rabbit population should rise, but what about the foxes should they rise as well that is where i am confused