Predator-Prey Model: Solving Equations & Plotting Results

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SUMMARY

The discussion focuses on the Predator-Prey Model represented by the differential equations dR/dt = aR - bRF and dF/dt = bRF - cF, where b is defined as b = b[SUB]o[SUB]*exp(-0.01*t*log(F)). The user observes typical oscillatory behavior in the populations initially, but later both species exhibit exponential growth, raising questions about the validity of the model and the impact of decreasing b on the populations. The primary inquiry is whether a decrease in b affects the growth of both rabbit (R) and fox (F) populations, indicating a need for clarity on the model's dynamics.

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  • Understanding of differential equations and their applications in biological modeling.
  • Familiarity with the Predator-Prey Model and its mathematical representation.
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Ecologists, mathematicians, and researchers interested in population dynamics, as well as students studying mathematical biology and differential equations.

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I modeled these equations

dR/dt = aR - bRF

dF/dt = bRF - cF where b = bo*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
 

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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
 

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