Maybe I'm getting things completely wrong, but the way I interpret your question you've plotted the last 2 components out of B returned bythe ODE-solver, and they grow in ways that "troubles" you?
If that's the case, then you've defined ODE-function such that the last two components of dBdt are alpha_a; alpha_m - meaning that the ode-solver returns the solution of the (components of the coupled ODE's) for the equations:
dF_1dt = alpha_a;
dF_2dt = alpha_m;
With alpha_a and alpha_m defined to be between 0 and 1 - this guarantees that F_1 and F_2 will grow for all times - maybe what you're interested in is the gradients of the F_1 and F_2 (last and second last component in your B) with respect to time - those would be your alpha_a and alpha_m.
HTH
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