|
|
This is only a preview of the paper
Click here to register and get the full text.
Existing members click here to login
|
|
|
The system we are offered to study, although having seemingly simple equations, that make sense in population growth, can produce very complex behavior. ...
In question 1, we are asked to consider the case when the predator population stays at P = 0. ... First, let’s introduce the predators and predation into our model, but let ε = 0. ... k only affects the size of the predator population (obviously, the larger, the better)! ... one prey population vanishes, although it does really come close to vanishing, the derivative of the solution curve is always positive at some point, and eventually, the solution has a sharp peak, after which it drops to around 0 again and the whole process repeats! ... ) doesn’t get the opportunity to kick in: for 100 < k < 312, the second species vanishes (see figure 14) (For 100 < k < 200 the predator population seems to vanish as well – the carrying capacity of the prey population is not sufficient to feed the predators). ... I tried again for k = 945 and I got all 3 population curves to plot out similar curves. ... We see that the prey population peaks behave much in the same manner, while the predator populations peaks behave differently. ... For lower values of k, the crowding has a strong effect for any solutions on the attractor, thus, if one prey population grows, the other necessarily shrinks. ... But this also means that the predator population doesn’t necessarily have to shrink in response to N2 population growing (usually, the ratio of desirable to undesirable prey would decrease). ...
This concludes the analysis of our population system.
Approximate Word count = 3550
Approximate Pages = 14.2
(250 words per page double spaced)
|
|
|
|
|
|